TY - JOUR
T1 - A confidence limit for the empirical mode decomposition and Hilbert spectral analysis
AU - Huang, Norden E.
AU - Wu, Man Li C.
AU - Long, Steven R.
AU - Shen, Samuel S.P.
AU - Qu, Wendong
AU - Gloersen, Per
AU - Fan, Kuang L.
PY - 2003/9/8
Y1 - 2003/9/8
N2 - The confidence limit is a standard measure of the accuracy of the result in any statistical analysis. Most of the confidence limits are derived as follows. The data are first divided into subsections and then, under the ergodic assumption, the temporal mean is substituted for the ensemble mean. Next, the confidence limit is defined as a range of standard deviations from this mean. However, such a confidence limit is valid only for linear and stationary processes. Furthermore, in order for the ergodic assumption to be valid, the subsections have to be statistically independent. For non-stationary and nonlinear processes, such an analysis is no longer valid. The confidence limit of the method here termed EMD/HSA (for empirical mode decomposition/ Hilbert spectral analysis) is introduced by using various adjustable stopping criteria in the sifting processes of the EMD step to generate a sample set of intrinsic mode functions (IMFs). The EMD technique acts as a pre-processor for HSA on the original data, producing a set of components (IMFs) from the original data that equal the original data when added back together. Each IMF represents a scale in the data, from smallest to largest. The ensemble mean and standard deviation of the IMF sample sets obtained with different stopping criteria are calculated, and these form a simple random sample set. The confidence limit for EMD/HSA is then defined as a range of standard deviations from the ensemble mean. Without evoking the ergodic assumption, subdivision of the data stream into short sections is unnecessary; hence, the results and the confidence limit retain the full-frequency resolution of the full dataset. This new confidence limit can be applied to the analysis of nonlinear and non-stationary processes by these new techniques. Data from length-of-day measurements and a particularly violent recent earthquake are used to demonstrate how the confidence limit is obtained and applied. By providing a confidence limit for this new approach, a stable range of stopping criteria for the decomposition or sifting phase (EMD) has been established, making the results of the final processing with HSA, and the entire EMD/HSA method, more definitive.
AB - The confidence limit is a standard measure of the accuracy of the result in any statistical analysis. Most of the confidence limits are derived as follows. The data are first divided into subsections and then, under the ergodic assumption, the temporal mean is substituted for the ensemble mean. Next, the confidence limit is defined as a range of standard deviations from this mean. However, such a confidence limit is valid only for linear and stationary processes. Furthermore, in order for the ergodic assumption to be valid, the subsections have to be statistically independent. For non-stationary and nonlinear processes, such an analysis is no longer valid. The confidence limit of the method here termed EMD/HSA (for empirical mode decomposition/ Hilbert spectral analysis) is introduced by using various adjustable stopping criteria in the sifting processes of the EMD step to generate a sample set of intrinsic mode functions (IMFs). The EMD technique acts as a pre-processor for HSA on the original data, producing a set of components (IMFs) from the original data that equal the original data when added back together. Each IMF represents a scale in the data, from smallest to largest. The ensemble mean and standard deviation of the IMF sample sets obtained with different stopping criteria are calculated, and these form a simple random sample set. The confidence limit for EMD/HSA is then defined as a range of standard deviations from the ensemble mean. Without evoking the ergodic assumption, subdivision of the data stream into short sections is unnecessary; hence, the results and the confidence limit retain the full-frequency resolution of the full dataset. This new confidence limit can be applied to the analysis of nonlinear and non-stationary processes by these new techniques. Data from length-of-day measurements and a particularly violent recent earthquake are used to demonstrate how the confidence limit is obtained and applied. By providing a confidence limit for this new approach, a stable range of stopping criteria for the decomposition or sifting phase (EMD) has been established, making the results of the final processing with HSA, and the entire EMD/HSA method, more definitive.
KW - EMD/HSA
KW - Empirical mode decomposition
KW - Hilbert spectral analysis
KW - Hilbert-Huang transform (HHT)
KW - Non-steady data analysis
KW - Nonlinear data analysis
UR - http://www.scopus.com/inward/record.url?scp=1542357546&partnerID=8YFLogxK
U2 - 10.1098/rspa.2003.1123
DO - 10.1098/rspa.2003.1123
M3 - 期刊論文
AN - SCOPUS:1542357546
SN - 1364-5021
VL - 459
SP - 2317
EP - 2345
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2037
ER -