Dong Wang

Entropy-Based Wavelet De-noising Method for Time Series Analysis

The existence of noise has great influence on the real features of observed time series, thus noise reduction in time series data is a necessary and significant task in many practical applications. When using traditional de-noising methods, the results often cannot meet the practical needs due to their inherent shortcomings. In the present paper, first a set of key but difficult wavelet de-noising problems are discussed, and then by applying information entropy theories to the wavelet de-noising process, i.e., using the principle of maximum entropy (POME) to describe the random character of the noise and using wavelet energy entropy to describe the degrees of complexity of the main series in original series data, a new entropy-based wavelet de-noising method is proposed. Analysis results of both several different synthetic series and typical observed time series data have verified the performance of the new method. A comprehensive discussion of the results indicates that compared with traditional wavelet de-noising methods, the new proposed method is more effective and universal. Furthermore, because it uses information entropy theories to describe the obviously different characteristics of noises and the main series in the series data is observed first and then de-noised, the analysis process has a more reliable physical basis, and the results of the new proposed method are more reasonable and are the global optimum. Besides, the analysis process of the new proposed method is simple and is easy to implement, so it would be more applicable and useful in applied sciences and practical engineering works.

Entropy-Based Method of Choosing the Decomposition Level in Wavelet Threshold De-noising

In this paper, the energy distributions of various noises following normal, log-normal and Pearson-III distributions are first described quantitatively using the wavelet energy entropy (WEE), and the results are compared and discussed. Then, on the basis of these analytic results, a method for use in choosing the decomposition level (DL) in wavelet threshold de-noising (WTD) is put forward. Finally, the performance of the proposed method is verified by analysis of both synthetic and observed series. Analytic results indicate that the proposed method is easy to operate and suitable for various signals. Moreover, contrary to traditional white noise testing which depends on “autocorrelations”, the proposed method uses energy distributions to distinguish real signals and noise in noisy series, therefore the chosen DL is reliable, and the WTD results of time series can be improved.

Wavelet-Based Analysis on the Complexity of Hydrologic Series Data under Multi-Temporal Scales

In this paper, the influence of four key issues on wavelet-based analysis of hydrologic series’ complexity under multi-temporal scales, including the choice of mother wavelet, noise, estimation of probability density function and trend of series data, was first studied. Then, the complexities of several representative hydrologic series data were quantified and described, based on which the performances of four wavelet-based entropy measures used commonly, namely continuous wavelet entropy (CWE), continuous wavelet relative entropy (CWRE), discrete wavelet entropy (DWE) and discrete wavelet relative entropy (DWRE) respectively, were compared and discussed. Finally, according to the analytic results of various examples, some understanding and conclusions about the calculation of wavelet-based entropy values gained in this study have been summarized, and the corresponding suggestions have also been proposed, based on which the analytic results of complexity of hydrologic series data can be improved.

Probabilistic Forecast and Uncertainty Assessment of Hydrologic Design Values Using Bayesian Theories

ABSTRACT Researches on hydrologic extreme events have great significance in reducing and avoiding the severe losses and impacts caused by natural disasters. When forecasting hydrologic design values of the hydrologic extreme events of interest by the conventional hydrologic frequency analysis (HFA) model, the results cannot take uncertainties and risks into account. In this article, in order to overcome conventional HFA models disadvantages and to improve hydrologic design values’ forecast results, an improved HFA model named AM-MCMC-HFA is proposed by employing the AM-MCMC algorithm (adaptive Metropolis-Markov chain Monte Carlo) to HFA process. Differing with conventional HFA model, which is seeking single optimal forecast result, the AM-MCMC-HFA model can not only get the optimal but also the probabilistic forecast results of hydrologic design values. By applying to two obviously different hydrologic series, the performances of the model proposed have been verified. Analysis results show that four factors have great influence on hydrologic design values’ reliability, and also indicate that AM-MCMC-HFA has the ability of assessing the uncertainties of parameters and hydrologic design values. Therefore, by using the AM-MCMC-HFA model, hydrologic designs tasks can be operated more reasonably, and more rational decisions can be made by governmental decision-makers and public in practice.

Accelerating Entropy Theory: New Approach to the Risks of Risk Analysis in Water Issues

IEA (International Energy Agency). 2006. World Energy Outlook 2006.Organisation for Economic Co-operation and Development and International Energy Agency, Paris, France IPCC (Intergovernmental Panel on Climate Change). 2008. Technical Paper on Climate Change and Water. IPCC-XXVIII/Doc. 13(8.IV.2008), Geneva, Switzerland. Available at http://www.ipcc.ch/meetings/session28/doc13.pdf Johnson BL. 2005. Global warming—An opportunity for visionary leadership. Hum Ecol Risk

Improved continuous wavelet analysis of variation in the dominant period of hydrological time series

Abstract Two key issues of continuous wavelet transform (CWT), the choice of wavelet basis function and the determination of analytic procedure of CWT, were studied and approaches to solve them proposed. Then, the improved CWT method was used to reveal the periodic characteristics of several typical hydrological series, including runoff and precipitation data measured at diverse sampling rates. Finally, the results of periods identified by three methods were compared, and the variation of the first main period (FMP) with length of the annual hydrological series was investigated. The results indicate that hydrological time series show both global and local characteristics. Comparatively, the latter are more complicated and difficult to describe, because of their frequent manifestations of irregular phenomena. Moreover, the variation of FMP just reflects the complicated local characteristics of the hydrological series. In summary, this study improves the understanding of complicated hydrological processes, whereas description and simulation of the local characteristics of hydrological series should be the focus of future research. Editor D. Koutsoyiannis Citation Sang, Y.F., Wang, D., Wu, J.-C., Zhu, Q.-P., and Wang, L., 2013. Improved continuous wavelet analysis of variation in the dominant period of hydrological time series. Hydrological Sciences Journal, 58 (1), 1–15.

Uncertainty Analysis of Decomposition Level Choice in Wavelet Threshold De-Noising

In this paper, the complexities of various noises, which are quantified by wavelet energy entropy (WEE) and differential coefficient of WEE (D(WEE)), were first analyzed and their uncertainties then estimated and described using confidence intervals. Then, quantitative criterion for judging the WEE and D(WEE) difference between noisy series and noise was put forward, based on which the decomposition level (DL) choice method in wavelet threshold de-noising proposed in 2010 by Sang et al. was improved. Finally, analytical results from examples verified the performance of the improved method, and also demonstrated its much wider applicability; moreover, the DL chosen using it is more reliable because of the fact that uncertainty is taken into consideration.

Sustainable Management of the Future Environment under Uncertainties and Risks

In this world, the only changeless thing is change (Zhu 2006). Uncertainties exist in every aspect of our lives and risk management has always been a vital topic in the world. Today there are so many greater uncertainties and challenges. We must face insecurity and risk better than ever. Just take some natural disasters in the last 6 years as examples, The Indian Ocean Tsunami in 2004, Hurricane Katrina in 2005, lasting southeast United States drought in 2007, the Mexico, India, Nepal, Bhutan, Benga flood in the same year, the devastating Sichuan Province China earthquake in 2008, the severe Myanmar cyclonic storm Nargis in 2008, Indonesia’s West Sumatra province earthquake in 2009, and powerful northwest China’s Gansu Province Zhouqu County mudslides in 2010, and so on. Nature imposes severe situations on the earth from time to time. All these disasters destroy natural resources, homes and other structures, and very often harm or kill people. In addition to natural disasters, the world also encounters the darkness of fatal disease, human calamities, terrorism, war, and so on such as H1N1 flu, the Perm Russian nightclub fire in 2009, the Gulf of Mexico oil spill in 2010, the “world economic crisis” that we have still undergone from 2008 to now, the 9/11 terrorist attacks, and the Iraq War. All the aforementioned disasters bring tremendous risks to us at all levels. Therefore, how to acquire sustainable management of the future environment under uncertainties and risks is the new challenge in the new decade.

An Improved Wavelet De-noising Method for Time Series Analysis

On the basis of discussing some key problems about wavelet de-noising as: choice of reasonable wavelet function, determination of reasonable wavelet coefficients thresholds and choice of suitable threshold processing-means, an improved wavelet de-noising method has been proposed. Then by Monte-Carlo tests, the validity of this method is verified. Analyses results show that compared with traditional methods (FT, SURE and MINMAX), this improved wavelet de-noising method is more accurate and reliable. Furthermore, because of based on information entropy theories to choose the reasonable wavelet coefficients thresholds, the de-noising results by the improved method are the global optimum.

Study on the WCC Method for Time Series Data Analysis

In this paper, based on reviews of the wavelet cross-correlation methods (WCC) used for time series analysis briefly, the wavelet cross-correlation degree (WCCD), which can be used to describe the cross-correlations of time series data in the whole time domain, has been defined, and meanwhile the method of drawing wavelet cross-correlation coefficients contour map has also been proposed, by which the integrated time-frequency analyses of cross-correlations of time series can be realized. By applied to analyze two observed time series, the superiority and effectiveness of WCC methods have been verified. Analyses results show that both global and local cross-correlations of time series can be analyzed accurately by WCC methods. Compared with traditional cross-correlation analysis methods, the WCC methods are more applicable and flexible since they can describe the cross-correlations of non-stationary time series under any time scales and any time delays effectively.