WT-FCTGN:A wavelet-enhanced fully connected time-gated neural network for complex noisy traffic flow modeling

Accurate forecasting of traffic flow provides a powerful traffic decision-making basis for an intelligent transportation system. However, the traffic data's complexity and fluctuation, as well as the noise produced during collecting information and summarizing original data of traffic flow, cause large errors in the traffic flow forecasting results. This article suggests a solution to the above mentioned issues and proposes a fully connected time-gated neural network based on wavelet reconstruction(WT-FCTGN). To eliminate the potential noise and strengthen the potential traffic trend in the data, we adopt the methods of wavelet reconstruction and periodic data introduction to preprocess the data. The model introduces fully connected time-series blocks to model all the information including time sequence information and fluctuation information in the flow of traffic, and establishes the time gate block to comprehend the periodic characteristics of the flow of traffic and predict its flow. The performance of the WT-FCTGN model is validated on the public Pe MS data set. The experimental results show that the WT-FCTGN model has higher accuracy, and its mean absolute error(MAE), mean absolute percentage error(MAPE) and root mean square error(RMSE) are obviously lower than those of the other algorithms. The robust experimental results prove that the WT-FCTGN model has good anti-noise ability.

Research on runoff variations based on wavelet analysis and wavelet neural network model： A case study of the Heihe River drainage basin （1944-2005）

The Heihe River drainage basin is one of the endangered ecological regions of China. The shortage of water resources is the bottleneck, which constrains the sustainable development of the region. Many scholars in China have done researches concerning this problem. Based on previous researches, this paper analyzed characteristics, tendencies, and causes of annual runoff variations in the Yingluo Gorge （1944-2005） and the Zhengyi Gorge （1954-2005）, which are the boundaries of the upper reaches, the middle reaches, and the lower reaches of the Heihe River drainage basin, by wavelet analysis, wavelet neural network model, and GIS spatial analysis. The results show that： （1） annual runoff variations of the Yingluo Gorge have principal periods of 7 years and 25 years, and its increasing rate is 1.04 m^3/s.10y; （2） annual runoff variations of the Zhengyi Gorge have principal periods of 6 years and 27 years, and its decreasing rate is 2.25 m^3/s.10y; （3） prediction results show that： during 2006-2015, annual runoff variations of the Yingluo and Zhengyi gorges have ascending tendencies, and the increasing rates are respectively 2.04 m^3/s.10y and 1.61 m^3/s.10y; （4） the increase of annual runoff in the Yingluo Gorge has causal relationship with increased temperature and precipitation in the upper reaches, and the decrease of annual runoff in the Zhengyi Gorge in the past decades was mainly caused by the increased human consumption of water resources in the middle researches. The study results will provide scientific basis for making rational use and allocation schemes of water resources in the Heihe River drainage basin.

Wavelet Neural Network Based on NARMA-L2 Model for Prediction of Thermal Characteristics in a Feed System

Research of thermal characteristics has been a key issue in the development of high-speed feed system. Most of the work carried out thus far is based on the principle of directly mapping the thermal error against the temperature of critical machine elements irrespective of the operating conditions. But recent researches show that different sets of operating parameters generated significantly different error values even though the temperature of the machine elements generated was similar. As such, it is important to develop a generic thermal error model which is capable of evaluating the positioning error induced by different operating parameters. This paper ultimately aims at the development of a comprehensive prediction model that can predict the thermal characteristics under different operating conditions （feeding speed, load and preload of ballscrew） in a feed system. A novel wavelet neural network based on feedback linearization autoregressive moving averaging （NARMA-L2） model is introduced to predict the temperature rise of sensitive points and thermal positioning errors considering the different operating conditions as the model inputs. Particle swarm optimization（PSO） algorithm is brought in as the training method. According to ISO230-2 Positioning Accuracy Measurement and ISO230-3 Thermal Effect Evaluation standards, experiments under different operating conditions were carried out on a self-made quasi high-speed feed system experimental bench HUST-FS-001 by using Pt100 as temperature sensor, and the positioning errors were measured by Heidenhain linear grating scale. The experiment results show that the recommended method can be used to predict temperature rise of sensitive points and thermal positioning errors with good accuracy. The work described in this paper lays a solid foundation of thermal error prediction and compensation in a feed system based on varying operating conditions and machine tool characteristics.

WAVELET ESTIMATION FOR JUMPS IN A HETEROSCEDASTIC REGRESSION MODEL

Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump points. Then a procedure is developed to estimate the jumps and jump heights. All estimators are proved to be consistent.

基于深度学习和小波分析的LSTM-Wavelet模型股价预测

针对股价数据具有高噪声、非线性和非平稳性等特征,使得股价精确预测非常困难的问题,提出小波-长短记忆网络(LSTM-Wavelet)模型应用于股价预测。首先,利用小波(Wavelet)分解降低金融时间序列的不稳定性,并分析小波系数的细节特征;接着,发挥长短记忆网络(LSTM)模型的优势,深层挖掘小波系数中的长期依赖关系,对分解后的各层小波系数分别建模预测;最后进行预测小波系数的数据重构。使用中石油近两年的股价数据进行实证分析,以每个交易日的开盘价、最高价、最低价、交易量为特征输入,预测当日中石油的收盘价。结果表明:相较于标准LSTM模型和小波-ARIMA(ARIMA-Wavelet)模型,提出的LSTM-Wavelet模型有更好的预测效果;通过小波分析将复杂股票数据,分解为长短记忆网络(LSTM)容易识别的小波系数,根据各层小波系数不同的数据特征进行分层预测,提高了预测精度。

JUMP DETECTION BY WAVELET IN NONLINEAR AUTOREGRESSIVE MODELS

Wavelets are applied to detection of the jump points of a regression function in nonlinear autoregressive model x(t) = T(x(t-1)) + epsilon t. By checking the empirical wavelet coefficients of the data,which have significantly large absolute values across fine scale levels, the number of the jump points and locations where the jumps occur are estimated. The jump heights are also estimated. All estimators are shown to be consistent. Wavelet method ia also applied to the threshold AR(1) model(TAR(1)). The simple estimators of the thresholds are given,which are shown to be consistent.

Wavelet neural network aerodynamic modeling from flight data based on pso algorithm with information sharing and velocity disturbance

For the accurate description of aerodynamic characteristics for aircraft,a wavelet neural network (WNN) aerodynamic modeling method from flight data,based on improved particle swarm optimization (PSO) algorithm with information sharing strategy and velocity disturbance operator,is proposed.In improved PSO algorithm,an information sharing strategy is used to avoid the premature convergence as much as possible;the velocity disturbance operator is adopted to jump out of this position once falling into the premature convergence.Simulations on lateral and longitudinal aerodynamic modeling for ATTAS (advanced technologies testing aircraft system) indicate that the proposed method can achieve the accuracy improvement of an order of magnitude compared with SPSO-WNN,and can converge to a satisfactory precision by only 60 120 iterations in contrast to SPSO-WNN with 6 times precocities in 200 times repetitive experiments using Morlet and Mexican hat wavelet functions.Furthermore,it is proved that the proposed method is feasible and effective for aerodynamic modeling from flight data.

Identification Scheme for Fractional Hammerstein Models With the Delayed Haar Wavelet

The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix(HWOM). To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods.

Network traffic prediction by a wavelet-based combined model

Network traffic prediction models can be grouped into two types, single models and combined ones. Combined models integrate several single models and thus can improve prediction accuracy. Based on wavelet transform, grey theory, and chaos theory, this paper proposes a novel combined model, wavelet-grey-chaos （WGC）, for network traffic prediction. In the WGC model, we develop a time series decomposition method without the boundary problem by modifying the standard à trous algorithm, decompose the network traffic into two parts, the residual part and the burst part to alleviate the accumulated error problem, and employ the grey model GM（1,1） and chaos model to predict the residual part and the burst part respectively. Simulation results on real network traffic show that the WGC model does improve prediction accuracy.

Hidden Markov model based epileptic seizure detection using tunable Q wavelet transform

Epilepsy is one of the most prevalent neurological disorders affecting 70 million people worldwide.The present work is focused on designing an efficient algorithm for automatic seizure detection by using electroencephalogram(EEG) as a noninvasive procedure to record neuronal activities in the brain.EEG signals' underlying dynamics are extracted to differentiate healthy and seizure EEG signals.Shannon entropy,collision entropy,transfer entropy,conditional probability,and Hjorth parameter features are extracted from subbands of tunable Q wavelet transform.Efficient decomposition level for different feature vector is selected using the Kruskal-Wallis test to achieve good classification.Different features are combined using the discriminant correlation analysis fusion technique to form a single fused feature vector.The accuracy of the proposed approach is higher for Q=2 and J=10.Transfer entropy is observed to be significant for different class combinations.Proposed approach achieved 100% accuracy in classifying healthy-seizure EEG signal using simple and robust features and hidden Markov model with less computation time.The proposed approach efficiency is evaluated in classifying seizure and non-seizure surface EEG signals.The system has achieved 96.87% accuracy in classifying surface seizure and nonseizure EEG segments using efficient features extracted from different J level.

The application of modeling and prediction with MRA wavelet network

As there are lots of non-linear systems in the real engineering, it is very important to do more researches on the modeling and prediction of non-linear systems. Based on the multi-resolution analysis (MRA) of wavelet theory, this paper combined the wavelet theory with neural network and established a MRA wavelet network with the scaling function and wavelet function as its neurons. From the analysis in the frequency domain, the results indicated that MRA wavelet network was better than other wavelet networks in the ability of approaching to the signals. An essential research was can:led out on modeling and prediction with MRA wavelet network in the non-linear system. Using the lengthwise sway data received from the experiment of ship model, a model of offline prediction was established and was applied to the short-time prediction of ship motion. The simulation results indicated that the forecasting model improved the prediction precision effectively, lengthened the forecasting time and had a better prediction results than that of AR linear model. The research indicates that it is feasible to use the MRA wavelet network in the short-time prediction of ship motion.

Hybrid Model Based on Wavelet Decomposition for Electricity Consumption Prediction

The effective supply of electricity is the basis of ensuring economic development and people's normal life. It is difficult to store electricity, as leading to the production and consumption must be completed simultaneously. Therefore, it is of great significance to accurately predict the demand for electricity consumption for the production planning of electricity and the normal operation of the society. In this paper, a hybrid model is constructed to predict the electricity consumption in China. The structural breaks test of monthly electricity consumption in China from January 2010 to December 2016 is carried out by using the structural breaks unit root test. Based on the existence of structura breaks, the electricity consumption data are decomposed into low-frequency and high-frequency components by wavelet model, and the separated low frequency signal and high frequency signal are predicted by autoregressive integrated moving average(ARIMA) and nonlinear autoregressive neural network(NAR), respectively. Therefore the wavelet-ARIMA-NAR hybrid model is constructed. In order to compare the effect of the hybrid model, the structural time series(STS) model is applied to predicting the electricity consumption. The results of prediction error test show that the hybrid model is more accurate for electricity consumption prediction.

Analytical Polarizable Continuum Model for Wavelets on NURBS Patches

This article concerns the application of wavelet techniques on molecular surfaces constituted of four-sided patches. The Polarizable Continuum Model, which is governed by the Poisson-Boltzmann equation, is treated by means of boundary integral equations. The media inside and outside the molecular surface consist respectively of the solute and the solvent. For a given electrically charged molecule, the principal unknown is the electrostatic solvation energy when the permittivity is specified. The wavelet basis functions are constructed on the unit square which are subsequently mapped onto the patches that are assumed to be isotropically shaped and to admit similar surface areas. The initial transmission problem is recast as an integral equation in term of both the single and the double layers. Domain decomposition preconditioner serves as acceleration of the linear solver of the single layer which is badly conditioned.

Wavelet Density Estimation and Statistical Evidences Role for a GARCH Model in the Weighted Distribution

We consider n observations from the GARCH-type model: Z = UY, where U and Y are independent random variables. We aim to estimate density function Y where Y have a weighted distribution. We determine a sharp upper bound of the associated mean integrated square error. We also make use of the measure of expected true evidence, so as to determine when model leads to a crisis and causes data to be lost.

Wavelet-Based Nonstationary Wind Speed Model in Dongting Lake Cable-Stayed Bridge

The wind-rain induced vibration phenomena in the Dongting Lake Bridge (DLB) can be observed every year, and the field measurements of wind speed data of the bridge are usually nonstationary. Nonstationary wind speed can be decomposed into a deterministic time-varying mean wind speed and a zero-mean stationary fluctuating wind speed component. By using wavelet transform (WT), the time-varying mean wind speed is extracted and a nonstationary wind speed model is proposed in this paper. The wind characteristics of turbulence intensity, integral scale and probability distribution of the bridge are calculated from the typical wind samples recorded by the two anemometers installed on the DLB using the proposed nonstationary wind speed model based on WT. The calculated results are compared with those calculated by the empirical mode decomposition (EMD) and traditional approaches. The compared results indicate that the wavelet-based nonstationary wind speed model is more reasonable and appropriate than the EMD-based nonstationary and traditional stationary models for characterizing wind speed in analysis of wind-rain-induced vibration of cables.

Statistical Modeling with a Hidden Markov Tree and High-resolution Interpolation for Spaceborne Radar Reflectivity in the Wavelet Domain

With the increasing availability of precipitation radar data from space,enhancement of the resolution of spaceborne precipitation observations is important,particularly for hazard prediction and climate modeling at local scales relevant to extreme precipitation intensities and gradients.In this paper,the statistical characteristics of radar precipitation reflectivity data are studied and modeled using a hidden Markov tree(HMT)in the wavelet domain.Then,a high-resolution interpolation algorithm is proposed for spaceborne radar reflectivity using the HMT model as prior information.Owing to the small and transient storm elements embedded in the larger and slowly varying elements,the radar precipitation data exhibit distinct multiscale statistical properties,including a non-Gaussian structure and scale-to-scale dependency.An HMT model can capture well the statistical properties of radar precipitation,where the wavelet coefficients in each sub-band are characterized as a Gaussian mixture model(GMM),and the wavelet coefficients from the coarse scale to fine scale are described using a multiscale Markov process.The state probabilities of the GMM are determined using the expectation maximization method,and other parameters,for instance,the variance decay parameters in the HMT model are learned and estimated from high-resolution ground radar reflectivity images.Using the prior model,the wavelet coefficients at finer scales are estimated using local Wiener filtering.The interpolation algorithm is validated using data from the precipitation radar onboard the Tropical Rainfall Measurement Mission satellite,and the reconstructed results are found to be able to enhance the spatial resolution while optimally reproducing the local extremes and gradients.

Wavelet Based Detection of Outliers in Volatility Time Series Models

We introduce a new wavelet based procedure for detecting outliers in financial discrete time series.The procedure focuses on the analysis of residuals obtained from a model fit,and applied to the Generalized Autoregressive Conditional Heteroskedasticity(GARCH)like model,but not limited to these models.We apply the Maximal-Overlap Discrete Wavelet Transform(MODWT)to the residuals and compare their wavelet coefficients against quantile thresholds to detect outliers.Our methodology has several advantages over existing methods that make use of the standard Discrete Wavelet Transform(DWT).The series sample size does not need to be a power of 2 and the transform can explore any wavelet filter and be run up to the desired level.Simulated wavelet quantiles from a Normal and Student t-distribution are used as threshold for the maximum of the absolute value of wavelet coefficients.The performance of the procedure is illustrated and applied to two real series:the closed price of the Saudi Stock market and the S&P 500 index respectively.The efficiency of the proposed method is demonstrated and can be considered as a distinct important addition to the existing methods.

Image denoising using statistical model based on quaternion wavelet domain

Image denoising is the basic problem of image processing. Quaternion wavelet transform is a new kind of multiresolution analysis tools. Image via quaternion wavelet transform, wavelet coefficients both in intrascale and in interscale have certain correla- tions. First, according to the correlation of quaternion wavelet coefficients in interscale, non-Ganssian distribution model is used to model its correlations, and the coefficients are divided into important and unimportance coefficients. Then we use the non-Gaussian distribution model to model the important coefficients and its adjacent coefficients, and utilize the MAP method estimate original image wavelet coefficients from noisy coefficients, so as to achieve the purpose of denoising. Experimental results show that our al- gorithm outperforms the other classical algorithms in peak signal-to-noise ratio and visual quality.

VARIABLE SELECTION BY PSEUDO WAVELETS IN HETEROSCEDASTIC REGRESSION MODELS INVOLVING TIME SERIES

A simple but efficient method has been proposed to select variables in heteroscedastic regression models. It is shown that the pseudo empirical wavelet coefficients corresponding to the significant explanatory variables in the regression models are clearly larger than those nonsignificant ones, on the basis of which a procedure is developed to select variables in regression models. The coefficients of the models are also estimated. All estimators are proved to be consistent.

WAVELET MODELING AND FORECASTING AND ITS APPLICATION IN THE CHINESE MONETARY MULTIPLIER

In this paper, a time_varying AR model is constructed by using the vector_space algorithm of compactly_supported biorthonormal wavelet transform. It is developed for forecasting narrow monetary multipliers in China .