scholarly journals Hybrid of the Lee-Carter Model with Maximum Overlap Discrete Wavelet Transform Filters in Forecasting Mortality Rates

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2295
Author(s):  
Nurul Aityqah Yaacob ◽  
Jamil J. Jaber ◽  
Dharini Pathmanathan ◽  
Sadam Alwadi ◽  
Ibrahim Mohamed
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Arima Model ◽  
Mortality Rates ◽  
Percentage Error ◽  
Mortality Data ◽  
Discrete Wavelet ◽  
Death Rates ◽  
Wavelet Filters ◽  
Carter Model

This study implements various, maximum overlap, discrete wavelet transform filters to model and forecast the time-dependent mortality index of the Lee-Carter model. The choice of appropriate wavelet filters is essential in effectively capturing the dynamics in a period. This cannot be accomplished by using the ARIMA model alone. In this paper, the ARIMA model is enhanced with the integration of various maximal overlap discrete wavelet transform filters such as the least asymmetric, best-localized, and Coiflet filters. These models are then applied to the mortality data of Australia, England, France, Japan, and USA. The accuracy of the projecting log of death rates of the MODWT-ARIMA model with the aforementioned wavelet filters are assessed using mean absolute error, mean absolute percentage error, and mean absolute scaled error. The MODWT-ARIMA (5,1,0) model with the BL14 filter gives the best fit to the log of death rates data for males, females, and total population, for all five countries studied. Implementing the MODWT leads towards improvement in the performance of the standard framework of the LC model in forecasting mortality rates.

MULTIVARIATE SPECTRAL ANALYSIS USING HILBERT WAVELET PAIRS

2004 ◽  
Vol 02 (04) ◽  
pp. 567-587 ◽  
Author(s):  
BRANDON WHITCHER ◽  
PETER F. CRAIGMILE
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Multivariate Time Series ◽  
Discrete Wavelet ◽  
Pass Filter ◽  
Wavelet Filters ◽  
The Hilbert Transform ◽  
High Pass

We investigate the use of Hilbert wavelet pairs (HWPs) in the non-decimated discrete wavelet transform for the time-varying spectral analysis of multivariate time series. HWPs consist of two high-pass and two low-pass compactly supported filters, such that one high-pass filter is the Hilbert transform (approximately) of the other. Thus, common quantities in the spectral analysis of time series (e.g., power spectrum, coherence, phase) may be estimated in both time and frequency. Compact support of the wavelet filters ensures that the frequency axis will be partitioned dyadically as with the usual discrete wavelet transform. The proposed methodology is used to analyze a bivariate time series of zonal (u) and meridional (v) winds over Truk Island.

Pre-Processing Influence on Identification of Optimal Path Length for NIR Analysis of Tea Polyphenols

2013 ◽  
Vol 791-793 ◽  
pp. 265-268
Author(s):  
Xiao Li Yang ◽  
Qiong He ◽  
Li Liu ◽  
Tong Yang
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Path Length ◽  
Near Infrared ◽  
Optimal Path ◽  
Tea Polyphenols ◽  
Percentage Error ◽  
Discrete Wavelet ◽  
Least Squares Regression ◽  
Path Lengths

We investigated the optical path length to tea polyphenols (TP) determination in Puer tea by near infrared (NIR) spectroscopy. The NIR spectra samples include three path lengths (1mm, 2mm and 5mm). Firstly, spectra were pre-processed to eliminate useless information. Then, determination model was constructed by partial least squares regression. To study the influence of pre-processing on identification of optimal path for NIR analysis of tea polyphenols, we applied five techniques to pre-process spectra, including normalization, standardization, centralization, derivative and discrete wavelet transform. Comparison of the mean absolute percentage error (MAPE) of the models with different path lengths show that the models constructed with spectra collected in 2mm path length gave the best results. 1mm path length gained the uncorrected determination results. Normalization, centralization and derivative are better than standardization or discrete wavelet transform for pre-processing.

scholarly journals Wind Power Short-Term Prediction Based on LSTM and Discrete Wavelet Transform

2019 ◽  
Vol 9 (6) ◽  
pp. 1108 ◽  
Author(s):  
Yao Liu ◽  
Lin Guan ◽  
Chen Hou ◽  
Hua Han ◽  
Zhangjie Liu ◽  
...  
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Wind Power ◽  
Short Term Memory ◽  
Wind Farms ◽  
Absolute Error ◽  
Percentage Error ◽  
Discrete Wavelet ◽  
Short Term

A wind power short-term forecasting method based on discrete wavelet transform and long short-term memory networks (DWT_LSTM) is proposed. The LSTM network is designed to effectively exhibit the dynamic behavior of the wind power time series. The discrete wavelet transform is introduced to decompose the non-stationary wind power time series into several components which have more stationarity and are easier to predict. Each component is dug by an independent LSTM. The forecasting results of the wind power are obtained by synthesizing the prediction values of all components. The prediction accuracy has been improved by the proposed method, which is validated by the MAE (mean absolute error), MAPE (mean absolute percentage error), and RMSE (root mean square error) of experimental results of three wind farms as the benchmarks. Wind power forecasting based on the proposed method provides an alternative way to improve the security and stability of the electric power network with the high penetration of wind power.

scholarly journals Fault location identification of double circuit transmission line using discrete wavelet transform

2019 ◽  
Vol 15 (3) ◽  
pp. 1356
Author(s):  
Abdul Hadi Bin Mustapha ◽  
R Hamdan ◽  
F. H. Mohd Noh ◽  
N. A. Zambri ◽  
M. H. A. Jalil ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Transmission Line ◽  
Fast Fourier Transform ◽  
Discrete Wavelet Transform ◽  
Fault Location ◽  
Detection Algorithm ◽  
Percentage Error ◽  
Discrete Wavelet ◽  
Fast Fourier Transform Algorithm

<span lang="EN-GB">The importance of supplying undisturbed electricity keep increasing due to modernization and lifestyle. Any disturbance in the power system may lead to discontinuation and degradation in the power quality. Therefore, detecting fault, fault type and fault location is a major issue in power transmission system in order to ensure reliable power delivery system. This paper will compare two prominent methods to estimate the fault location of double circuit transmission line. Those methods are Discrete Wavelet Transform algorithm and Fast Fourier Transform algorithm. Simulations has been carried out in MATLAB/Simulink and a variety of fault has been imposed in order to analyse the capability and accuracy of the fault location detection algorithm. Results obtained portrayed that both algorithms provide good performance in estimating the fault location. However, the maximum percentage error produced by the Discrete Wavelet Transform is only 0.25%, 0.6% lower than maximum error produces by Fast Fourier Transform algorithm. As a conclusion, Discrete Wavelet Transform possesses better capability to estimate fault location as compared to Fast Fourier Transform algorithm.</span>

scholarly journals Electrical Energy Demand Forecasting Model Development and Evaluation with Maximum Overlap Discrete Wavelet Transform-Online Sequential Extreme Learning Machines Algorithms

Energies ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2307
Author(s):  
Mohanad S. Al-Musaylh ◽  
Ravinesh C. Deo ◽  
Yan Li
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Electricity Markets ◽  
Energy Demand ◽  
Time Series Data ◽  
Demand Forecasting ◽  
Model Development ◽  
Series Data ◽  
Percentage Error ◽  
Discrete Wavelet

To support regional electricity markets, accurate and reliable energy demand (G) forecast models are vital stratagems for stakeholders in this sector. An online sequential extreme learning machine (OS-ELM) model integrated with a maximum overlap discrete wavelet transform (MODWT) algorithm was developed using daily G data obtained from three regional campuses (i.e., Toowoomba, Ipswich, and Springfield) at the University of Southern Queensland, Australia. In training the objective and benchmark models, the partial autocorrelation function (PACF) was first employed to select the most significant lagged input variables that captured historical fluctuations in the G time-series data. To address the challenges of non-stationarities associated with the model development datasets, a MODWT technique was adopted to decompose the potential model inputs into their wavelet and scaling coefficients before executing the OS-ELM model. The MODWT-PACF-OS-ELM (MPOE) performance was tested and compared with the non-wavelet equivalent based on the PACF-OS-ELM (POE) model using a range of statistical metrics, including, but not limited to, the mean absolute percentage error (MAPE%). For all of the three datasets, a significantly greater accuracy was achieved with the MPOE model relative to the POE model resulting in an MAPE = 4.31% vs. MAPE = 11.31%, respectively, for the case of the Toowoomba dataset, and a similarly high performance for the other two campuses. Therefore, considering the high efficacy of the proposed methodology, the study claims that the OS-ELM model performance can be improved quite significantly by integrating the model with the MODWT algorithm.

scholarly journals A Novel Method for Regional NO2 Concentration Prediction Using Discrete Wavelet Transform and an LSTM Network

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Bingchun Liu ◽  
Lei Zhang ◽  
Qingshan Wang ◽  
Jiali Chen
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Input Data ◽  
Short Term Memory ◽  
Meteorological Data ◽  
Atmospheric Pollutants ◽  
Percentage Error ◽  
Support Vector ◽  
Discrete Wavelet ◽  
Lstm Network

Achieving accurate predictions of urban NO2 concentration is essential for effectively control of air pollution. This paper selected the concentration of NO2 in Tianjin as the research object, concentrating predicting model based on Discrete Wavelet Transform and Long- and Short-Term Memory network (DWT-LSTM) for predicting daily average NO2 concentration. Five major atmospheric pollutants, key meteorological data, and historical data were selected as the input indexes, realizing the effective prediction of NO2 concentration in the next day. Firstly, the input data were decomposed by Discrete Wavelet Transform to increase the data dimension. Furthermore, the LSTM network model was used to learn the features of the decomposed data. Ultimately, Support Vector Regression (SVR), Gated Regression Unit (GRU), and single LSTM model were selected as comparison models, and each performance was evaluated by the Mean Absolute Percentage Error (MAPE). The results show that the DWT-LSTM model constructed in this paper can improve the accuracy and generalization ability of data mining by decomposing the input data into multiple components. Compared with the other three methods, the model structure is more suitable for predicting NO2 concentration in Tianjin.

scholarly journals Analysis of the Quantization Noise in Discrete Wavelet Transform Filters for 3D Medical Imaging

2020 ◽  
Vol 10 (4) ◽  
pp. 1223 ◽  
Author(s):  
Nikolay Chervyakov ◽  
Pavel Lyakhov ◽  
Nikolay Nagornov
Keyword(s):  
Wavelet Transform ◽  
Medical Imaging ◽  
Integrated Circuits ◽  
Discrete Wavelet Transform ◽  
Signal To Noise Ratio ◽  
Maximum Error ◽  
Quantization Noise ◽  
Discrete Wavelet ◽  
Wavelet Filters ◽  
Images Processing

Denoising and compression of 2D and 3D images are important problems in modern medical imaging systems. Discrete wavelet transform (DWT) is used to solve them in practice. We analyze the quantization noise effect in coefficients of DWT filters for 3D medical imaging in this paper. The method for wavelet filters coefficients quantizing is proposed, which allows minimizing resources in hardware implementation by simplifying rounding operations. We develop the method for estimating the maximum error of 3D grayscale and color images DWT with various bits per color (BPC). The dependence of the peak signal-to-noise ratio (PSNR) of the images processing result on wavelet used, the effective bit-width of filters coefficients and BPC is revealed. We derive formulas for determining the minimum bit-width of wavelet filters coefficients that provide a high (PSNR ≥ 40 dB for images with 8 BPC, for example) and maximum (PSNR = ∞ dB) quality of 3D medical imaging by DWT depending on wavelet used. The experiments of 3D tomographic images processing confirmed the accuracy of theoretical analysis. All data are presented in the fixed-point format in the proposed method of 3D medical images DWT. It is making possible efficient, from the point of view of hardware and time resources, the implementation for image denoising and compression on modern devices such as field-programmable gate arrays and application-specific integrated circuits.

TWO-DIMENSIONAL STATIONARY DYADIC WAVELET TRANSFORM, DECIMATED DYADIC DISCRETE WAVELET TRANSFORM AND THE FACE RECOGNITION APPLICATION

2011 ◽  
Vol 09 (03) ◽  
pp. 397-416 ◽  
Author(s):  
YANKUI SUN ◽  
YONG CHEN ◽  
HAO FENG
Keyword(s):  
Face Recognition ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Recognition Algorithm ◽  
Discrete Wavelet ◽  
Two Dimensional ◽  
Wavelet Filters ◽  
Dyadic Wavelet ◽  
Dyadic Wavelet Transform ◽  
Approximation Coefficients

Currently, two-dimensional dyadic wavelet transform (2D-DWT) is habitually considered as the one presented by Mallat, which is defined by an approximation component, two detail components in horizontal and vertical directions. This paper is to introduce a new type of two-dimensional dyadic wavelet transform and its application so that dyadic wavelet can be studied and used widely furthermore. (1) Two-dimensional stationary dyadic wavelet transform (2D-SDWT) is proposed, it is defined by approximation coefficients, detail coefficients in horizontal, vertical and diagonal directions, which is essentially the extension of two-dimensional stationary wavelet transform for orthogonal/biorthogonal wavelet filters. (2) ε-decimated dyadic discrete wavelet transform (DDWT) is introduced and its relation with 2D-SDWT is given, where ε is a sequence of 0's and 1's. (3) Mallat decomposition algorithm based on dyadic wavelet is introduced as a special case of ε-decimated DDWT, and so a face recognition algorithm based on dyadic wavelet is proposed, and experimental results are given to show its effectiveness.

scholarly journals A Hybrid Arima and Discrete Wavelet Transform Model for Predicting the Electricity Consumption of Punjab

2019 ◽  
Vol 8 (11) ◽  
pp. 1915-1919
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Arima Model ◽  
Electricity Consumption ◽  
Electricity Production ◽  
Series Data ◽  
Support Vector ◽  
Discrete Wavelet ◽  
World Population ◽  
Proposed Model

The significant increase in the world population increases the demand for energy which seems to be alarming for the electricity production boards in the existing time. In the last decade, there are various engineering, simulation tools, and artificial intelligence-based methods such as Support Vector Machine and Artificial Neural Network proposed in the literature to forecast the optimal electricity demand. But these models seldom to work with the linear data. In this paper, a reliable prediction model using the linear time series data of the previous years from January 2013 to December 2017 has been presented to forecast the electricity consumption in Punjab, India. Initially, Discrete Wavelet Transform (DWT) analysis presented to extract the upper and lower limit of the previous year dataand then AutoRegressive Integrated Moving Average (ARIMA) model has been applied to extract the forecast values. The experimental results compared the original and predicted value using the proposed model to evaluate the effectiveness of the proposed approach. The results show that the difference between the original and proposed modelis only 9% while that of ARIMA only it is 11%. Thus, the proposed model using ARIMA and DWT provides effective results in predicting the forecast value.

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