One remarkable feature of wavelet decomposition is that the waveletcoefficients are localized, and any singularity in the input signals can only affect the waveletcoefficients at the point near the singularity. The lo...One remarkable feature of wavelet decomposition is that the waveletcoefficients are localized, and any singularity in the input signals can only affect the waveletcoefficients at the point near the singularity. The localized property of the wavelet coefficientsallows us to identify the singularities in the input signals by studying the wavelet coefficients atdifferent resolution levels. This paper considers wavelet-based approaches for the detection ofoutliers in time series. Outliers are high-frequency phenomena which are associated with the waveletcoefficients with large absolute values at different resolution levels. On the basis of thefirst-level wavelet coefficients, this paper presents a diagnostic to identify outliers in a timeseries. Under the null hypothesis that there is no outlier, the proposed diagnostic is distributedas a χ_1~2. Empirical examples are presented to demonstrate the application of the proposeddiagnostic.展开更多
We proposed and demonstrated a wavelet transform modulus maxima （WTMM） de-noising method to decrease the temperature error. In this scheme, the composition scale was determined simply by the WTMM amplitude variation...We proposed and demonstrated a wavelet transform modulus maxima （WTMM） de-noising method to decrease the temperature error. In this scheme, the composition scale was determined simply by the WTMM amplitude variation with the growth of the decomposition scale at 30 ℃, and the signal WTMM was obtained by the wavelet decomposition modulus on every decomposition scale based on the modulus propagating difference between the signal and noise. Then, we reconstructed the signal using the signal WTMM. Experimental results show that the proposed method is effective for de-noising, allowing for a temperature error decrease of about 1 ℃ at 40 ℃ and 50℃ comparing to the original data.展开更多
基金This research is supportea by the National Natural Science Foundation of China (79800012,70171001)
文摘One remarkable feature of wavelet decomposition is that the waveletcoefficients are localized, and any singularity in the input signals can only affect the waveletcoefficients at the point near the singularity. The localized property of the wavelet coefficientsallows us to identify the singularities in the input signals by studying the wavelet coefficients atdifferent resolution levels. This paper considers wavelet-based approaches for the detection ofoutliers in time series. Outliers are high-frequency phenomena which are associated with the waveletcoefficients with large absolute values at different resolution levels. On the basis of thefirst-level wavelet coefficients, this paper presents a diagnostic to identify outliers in a timeseries. Under the null hypothesis that there is no outlier, the proposed diagnostic is distributedas a χ_1~2. Empirical examples are presented to demonstrate the application of the proposeddiagnostic.
基金This work was supported by the Natural Science Foundation of China （60977058 ＆ 61307101）, Independent Innovation Foundation of Shandong University （IIFSDU2012JC015） and the key technology projects of Shandong Province （2010GGX10137）.
文摘We proposed and demonstrated a wavelet transform modulus maxima （WTMM） de-noising method to decrease the temperature error. In this scheme, the composition scale was determined simply by the WTMM amplitude variation with the growth of the decomposition scale at 30 ℃, and the signal WTMM was obtained by the wavelet decomposition modulus on every decomposition scale based on the modulus propagating difference between the signal and noise. Then, we reconstructed the signal using the signal WTMM. Experimental results show that the proposed method is effective for de-noising, allowing for a temperature error decrease of about 1 ℃ at 40 ℃ and 50℃ comparing to the original data.
