Correcting data from an unknown accelerometer using recursive least squares and wavelet de-noising

Chanerley, AA; Alexander, Nicholas A.

doi:10.1016/j.compstruc.2007.02.025

Cited by 37 publications

(15 citation statements)

References 17 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As is known, hydrologic and meteorologic series are complicated. Although some papers [ Chanerley and Alexander , ; Sang , ] mentioned the issue on the choice of mother function for wavelet transform, there are no recognized method of how to choose this mother function. According to the former study, a universal criterion, trial‐and‐error method, is often used, which means adjusting measures and choosing a most suitable one in the family of frequently used mother function to local conditions of the given hydrologic and meteorologic series.…”

Section: Methodsmentioning

confidence: 99%

A hybrid wavelet analysis–cloud model data‐extending approach for meteorologic and hydrologic time series

et al. 2015

View full text Add to dashboard Cite

For scientific and sustainable management of water resources, hydrologic and meteorologic data series need to be often extended. This paper proposes a hybrid approach, named WA-CM (wavelet analysis-cloud model), for data series extension. Wavelet analysis has time-frequency localization features, known as "mathematics microscope," that can decompose and reconstruct hydrologic and meteorologic series by wavelet transform. The cloud model is a mathematical representation of fuzziness and randomness and has strong robustness for uncertain data. The WA-CM approach first employs the wavelet transform to decompose the measured nonstationary series and then uses the cloud model to develop an extension model for each decomposition layer series. The final extension is obtained by summing the results of extension of each layer. Two kinds of meteorologic and hydrologic data sets with different characteristics and different influence of human activity from six (three pairs) representative stations are used to illustrate the WA-CM approach. The approach is also compared with four other methods, which are conventional correlation extension method, Kendall-Theil robust line method, artificial neural network method (back propagation, multilayer perceptron, and radial basis function), and single cloud model method. To evaluate the model performance completely and thoroughly, five measures are used, which are relative error, mean relative error, standard deviation of relative error, root mean square error, and Thiel inequality coefficient. Results show that the WA-CM approach is effective, feasible, and accurate and is found to be better than other four methods compared. The theory employed and the approach developed here can be applied to extension of data in other areas as well.

show abstract

Section: Methodsmentioning

confidence: 99%

A hybrid wavelet analysis–cloud model data‐extending approach for meteorologic and hydrologic time series

et al. 2015

View full text Add to dashboard Cite

show abstract

“…The core of wavelet de‐noised method is to select a reasonable threshold value, which is directly related to the quality of de‐noising. There are several conventional methods for choosing a suitable threshold value, such as FT, SURE, or MINMAX [ Donoho , ; Bruni and Vitulano , ; Chanerley and Alexander , ].…”

Section: Wavelet De‐noising Methodsmentioning

confidence: 99%

Sample entropy‐based adaptive wavelet de‐noising approach for meteorologic and hydrologic time series

et al. 2014

View full text Add to dashboard Cite

De-noising meteorologic and hydrologic time series is important to improve the accuracy and reliability of extraction, analysis, simulation, and forecasting. A hybrid approach, combining sample entropy and wavelet de-noising method, is developed to separate noise from original series and is named as AWDA-SE (adaptive wavelet de-noising approach using sample entropy). The AWDA-SE approach adaptively determines the threshold for wavelet analysis. Two kinds of meteorologic and hydrologic data sets, synthetic data set and 3 representative field measured data sets (one is the annual rainfall data of Jinan station and the other two are annual streamflow series from two typical stations in China, Yingluoxia station on the Heihe River, which is little affected by human activities, and Lijin station on the Yellow River, which is greatly affected by human activities), are used to illustrate the approach. The AWDA-SE approach is compared with three conventional de-noising methods, including fixed-form threshold algorithm, Stein unbiased risk estimation algorithm, and minimax algorithm. Results show that the AWDA-SE approach separates effectively the signal and noise of the data sets and is found to be better than the conventional methods. Measures of assessment standards show that the developed approach can be employed to investigate noisy and short time series and can also be applied to other areas.

show abstract

“…Based on this difference, proper thresholds can be used to adjust the wavelet coefficients of DWT, and then the main series and noises can be separated by using the wavelet reconstruction method. This is the basic idea of wavelet threshold de-nosing [9,19,53,54]. There are four main and key problems in the wavelet de-noising process, namely: (1) choice of reasonable wavelet functions and (2) choice of proper time scale levels, both of which mainly determine the accuracy and reasonability of the DWT results; (3) determination of accurate thresholds under each time scale level by certain methods; and (4) choice of suitable thresholding rules.…”

Section: Traditional Wavelet De-noising Methodsmentioning

confidence: 99%

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

Sang

Wang

et al. 2009

Entropy

View full text Add to dashboard Cite

Abstract: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 OPEN ACCESSEntropy 2009, 11 1124 to implement, so it would be more applicable and useful in applied sciences and practical engineering works.

show abstract

Correcting data from an unknown accelerometer using recursive least squares and wavelet de-noising

Cited by 37 publications

References 17 publications

A hybrid wavelet analysis–cloud model data‐extending approach for meteorologic and hydrologic time series

A hybrid wavelet analysis–cloud model data‐extending approach for meteorologic and hydrologic time series

Sample entropy‐based adaptive wavelet de‐noising approach for meteorologic and hydrologic time series

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

Contact Info

Product

Resources

About