CHARACTERIZATIONS OF FUNDAMENTAL SCALING FUNCTIONS AND WAVELETS

The objective of Ibis paper is to establish precise characterizations of scaling functions which are orthonormal or fundamental.A criterion for the corresponding wavelets is also given.

Wavelet-Based Fractal Function Approximation

In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression.

Cylindrical Guided Wave Signals for Underground Pipe Inspection using Different Continuous Wavelet Mother Functions

Over the past decade, wavelets provided a powerful and flexible set of tools for handling fundamental problems in science and engineering. Wavelet analyses are being used for solving problems in different engineering areas like audio de-noising, signal compression, object detection, image decomposition, speech recognition etc. Wavelet analysis employs orthonormal as well as non-orthonornal functions. This research investigates the effectiveness of wavelet analysis in detecting defects in underground steel pipe networks. Continuous Wavelet Transforms （CWT） has been performed on the received signals of cylindrical guided waves. Cylindrical Guided waves are generated and propagated through the pipe wall boundaries in a pitch-catch system. Piezo-electric transducers are used to generate as well as receive guided waves. Several mother wavelet functions such as Daubechies, Symlet, Coiflet and Meyer have been used for the Continuous Wavelet Transform to investigate the most suitable function for defect detection. This research also investigates the effect of surrounding soil on wavelet transforms for different mother wavelet functions.

Wavelets applied to early fault analysis of hoist gear box

Using wavelets, the vibration signal of a certain mine hoist gear box was analyzed. By multiple comparison analysis, the rational wavelet basis function was determined. Fault characteristic frequencies of hoist gear box were identified. The research indicates that the hoist＇s fault information is non-stationary, and non-stationary signal is clearly extracted by using db20 wavelet as basis function. The db20 wavelet is the proper wavelet base for vibration signal analysis of the hoist gear box.

Investigation of the Tikhonov Regularization Method in Regional Gravity Field Modeling by Poisson Wavelets Radial Basis Functions

The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.

Simulation and prediction of monthly accumulated runoff,based on several neural network models under poor data availability

Most previous research on areas with abundant rainfall shows that simulations using rainfall-runoff modes have a very high prediction accuracy and applicability when using a back-propagation(BP), feed-forward, multilayer perceptron artificial neural network(ANN). However, in runoff areas with relatively low rainfall or a dry climate, more studies are needed. In these areas—of which oasis-plain areas are a particularly good example—the existence and development of runoff depends largely on that which is generated from alpine regions. Quantitative analysis of the uncertainty of runoff simulation under climate change is the key to improving the utilization and management of water resources in arid areas. Therefore, in this context, three kinds of BP feed-forward, three-layer ANNs with similar structure were chosen as models in this paper.Taking the oasis–plain region traverse by the Qira River Basin in Xinjiang, China, as the research area, the monthly accumulated runoff of the Qira River in the next month was simulated and predicted. The results showed that the training precision of a compact wavelet neural network is low; but from the forecasting results, it could be concluded that the training algorithm can better reflect the whole law of samples. The traditional artificial neural network(TANN) model and radial basis-function neural network(RBFNN) model showed higher accuracy in the training and prediction stage. However, the TANN model, more sensitive to the selection of input variables, requires a large number of numerical simulations to determine the appropriate input variables and the number of hidden-layer neurons. Hence, The RBFNN model is more suitable for the study of such problems. And it can be extended to other similar research arid-oasis areas on the southern edge of the Kunlun Mountains and provides a reference for sustainable water-resource management of arid-oasis areas.

Denoising Method for Partial Discharge Signal of Switchgear Based on Continuous Adaptive Wavelet Threshold

Partial discharge(PD)is an important reason for the insulation failure of the switchgear.In the process of PD detection,PD signal is often annihilated in strong noise.In order to improve the accuracy of PD detection in power plant switchgear,a method based on continuous adaptive wavelet threshold switchgear PD signals denoising is proposed in this paper.By constructing a continuous adaptive threshold function and introducing adjustment parameters,the problems of over⁃processing of traditional hard threshold functions and incomplete denoising of soft threshold functions can be improved.The analysis results of simulated signals and measured signals show that the continuous adaptive wavelet threshold denoising method is significantly better than the traditional denoising method for the PD signal.The proposed method in this paper retains the characteristics of the original signal.Compared with the traditional denoising methods,after denoising the simulated signals,the signal⁃to⁃noise ratio(SNR)is increased by more than 30%,and the root⁃mean⁃square error(RMSE)is reduced by more than 30%.After denoising the real signal,the noise suppression ratio(NRR)is increased by more than 40%.The recognition accuracy rate of PD signal has also been improved to a certain extent,which proves that the method has a certain practicability.

WAVELET KERNEL SUPPORT VECTOR MACHINES FOR SPARSE APPROXIMATION

Wavelet, a powerful tool for signal processing, can be used to approximate the target func-tion. For enhancing the sparse property of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support Vector Machines (SVM), which can converge to minimum error with bet-ter sparsity. Here, wavelet functions would be firstly used to construct the admitted kernel for SVM according to Mercy theory; then new SVM with this kernel can be used to approximate the target fun-citon with better sparsity than wavelet approxiamtion itself. The results obtained by our simulation ex-periment show the feasibility and validity of wavelet kernel support vector machines.

WRIST FORCE SENSOR'S DYNAMIC PERFORMANCE CALIBRATION BASED ON NEGATIVE STEP RESPONSE

Negative step response experimental method is used in wrist force sensor＇s dynamic performance calibration. The exciting manner of negative step response method is the same as wrist force sensor＇s load in working. This experimental method needn＇t special experiment equipments. Experiment＇s dynamic repeatability is good. So wrist force sensor＇s dynamic performance is suitable to be calibrated by negative step response method. A new correlation wavelet transfer method is studied. By wavelet transfer method, the signal is decomposed into two dimensional spaces of time-frequency. So the problem of negative step exciting energy concentrating in the low frequency band is solved. Correlation wavelet transfer doesn＇t require that wavelet primary function be orthogonal and needn＇t wavelet reconstruction. So analyzing efficiency is high. An experimental bench is designed and manufactured to load the wrist force sensor orthogonal excitation force/moment. A piezoelectric force sensor is used to setup soft trigger and calculate the value of negative step excitation. A wrist force sensor is calibrated. The pulse response function is calculated after negative step excitation and step response have been transformed to positive step excitation and step response. The pulse response function is transferred to frequency response function. The wrist force sensor＇s dynamic characteristics are identified by the frequency response function.

Analysis on observational results of Pi2 geomagnetic pulsation in Henan region

A measurement profile consisted of 5 sites from Xinyang to Tangyin in Henan Province was set up in September of 1996 to carry out simultaneous observation of Pi2 geomagnetic pulsations. Simultaneity of Pi2 geomagnetic pulsation occurrence along the N-S profile was investigated. Results of analysis pointed out that Pi2 gcomagnetic pulsations appeared at first at the site of Xinyang at the southern end of the profile, the later the same Pi2 geomag netic pulsation appeared, the more north the site was at. Apparent propagation speed of Pi2 in N-S direction in the region is about 140 kin/s. Because Pi2 geomagnetic pulsation varying with time is of instability, and based on characteristics that basic wavelet can be dilated and localized, we selected proper basic wavelat form and by means of wavelet transform to analyze the changes of periods and amplitudes of main periodic components included in Pi2 pulsations with time. The results show that there existed complex form in periods and amplitudes of wavelet varying with time.

Interpretation of the short period variations in geomagnetic anomalies of Shaanxi region

A temporary profile from Shiquan in the southern part of Shaanxi Province to Ningxian in Gansu Province for observation of geomagnetic short period variations was set up. The characteristics of geomagnetic short period variations in the profile region was analyzed through geomagnetic transfer functions at measurement sites (Fan, et al, 1998). According to the theory of multi-scale analysis of wavelet transform, the components affected by regional origin in the region is extracted in this paper. The components of regional origin is used as original data in the inversion study for investigation of 2-D conductivity structure corresponding to the regional origin. The inversion method (Zhdanov, Traynin, 1997) which is based on the minimum of the total energy of the residual field between observational electro-magnetic field and the calculated theoretical field of conductivity model and the conception of migrated residual field is introduced into our inversion of the data of magneto-variation sounding. The result of the inversion gives the underground conductivity structure in depth range of 100 km beneath the profile, and shows that a high conductivity area is located under Wugong and Qianling. The main characteristics of the inversion method is briefly discussed, that is, it can reflect the depth and the distribution of anomalous conductivity area comparatively well, and large number of parameters of inversion model is allowed to be used in the Inversion.

Traffic Sign Recognition Based on CNN and Twin Support Vector Machine Hybrid Model

With the progress of deep learning research, convolutional neural networks have become the most important method in feature extraction. How to effectively classify and recognize the extracted features will directly affect the performance of the entire network. Traditional processing methods include classification models such as fully connected network models and support vector machines. In order to solve the problem that the traditional convolutional neural network is prone to over-fitting for the classification of small samples, a CNN-TWSVM hybrid model was proposed by fusing the twin support vector machine (TWSVM) with higher computational efficiency as the CNN classifier, and it was applied to the traffic sign recognition task. In order to improve the generalization ability of the model, the wavelet kernel function is introduced to deal with the nonlinear classification task. The method uses the network initialized from the ImageNet dataset to fine-tune the specific domain and intercept the inner layer of the network to extract the high abstract features of the traffic sign image. Finally, the TWSVM based on wavelet kernel function is used to identify the traffic signs, so as to effectively solve the over-fitting problem of traffic signs classification. On GTSRB and BELGIUMTS datasets, the validity and generalization ability of the improved model is verified by comparing with different kernel functions and different SVM classifiers.

Parameterization of 3-channel non-separable 2-D wavelets and filters

We propose a complete parameterization presentation of the 3-channelbivariate non-separable orthogonal FIR filter, and describe the sufficient condition ofgenerating continuous wavelet bases. Given the results above, a non-separable,compactly supported, orthogonal, continuous parameterized bivariate wavelet bank is setup here.

DDoS detection based on wavelet kernel support vector machine

To enhance the detection accuracy and deduce false positive rate of distributed denial of service （DDoS） attack detection, a new machine learning method was proposed. With the analysis of support vector machine （SVM） and the wavelet kernel function theory, an admissive support vector kernel, which is a wavelet kernel constructed in this article, implements the combination of the wavelet technique with SVM. Then, wavelet support vector machine （WSVM） is applied to DDoS attack detections and as a classifying means to test the validity of the wavelet kernel function. Simulation experiments show that under the same conditions, the predictive ability of WSVM is improved and the computation burden is alleviated. The detection accuracy of WSVM is higher than the traditional SVM by about 4%, while its false positive is lower than the traditional SVM. Thus, for DDoS detections, WSVM shows better detection performance and is more adaptive to the changing network environment.

THE NUMERICAL METHODS FOR SOLVING EULER SYSTEM OF EQUATIONS IN REPRODUCING KERNEL SPACE H^2(R)

Provides information on a study which presented a numerical method for solving Euler system of equations in reproducing kernel space. Definition and properties of reproducing kernel space; Construction of reproducing kernel finite difference method; Numerical results of the study.

Modeling of coal consumption rate based on wavelet neural network

In this paper,two wavelet neural network(WNN)frames which depend on Morlet wavelet function and Gaussian wavelet function were established.In order to improve the efficiency of model training,the momentum term was applied to modify the weights and thresholds,and the output of the network was summed up by function transformation of output layer nodes.When the Gaussian Wavelet Neural Networks(GWNN)and Morlet Wavelet Neural Networks(MWNN)were applied to coal consumption rate(CCR)estimation in a thermal power plant,the results confirmed their potency in function approximation.In addition,the influence of learning rate on the models was also discussed through the orthogonal experiment.

New wavelet method for solving boundary value problems arising from an adiabatic tubular chemical reactor theory

This paper displays an efficient numerical technique of realizing mathematical models for an adiabatic tubular chemical reactor which forms an irreversible exothermic chemical reaction.At a steady-state solution for an adiabatic rounded reactor,the model can be diminished to a conventional nonlinear differential equation which converts into a system of the nonlinear equation that can proceed numerically utilizing Newton’s iterative method.An operational matrix of coordination is derived and is utilized to decrease the model for an adiabatic tubular chemical reactor to an arrangement of algebraic equations.Simple execution,basic activities,and precise arrangements are the fundamental highlights of the proposed wavelet technique.The numerical solutions attained by the present technique have been contrasted and compared with other techniques.

Improved single image dehazing using dark channel prior

An improved single image dehazing method based on dark channel prior and wavelet transform is proposed. This proposed method employs wavelet transform and guided filter instead of the soft matting procedure to estimate and refine the depth map of haze images. Moreover, a contrast enhancement method based on just noticeable difference(JND) and quadratic function is adopted to enhance the contrast for the dehazed image, since the scene radiance is usually not as bright as the atmospheric light,and the dehazed image looks dim. The experimental results show that the proposed approach can effectively enhance the haze image and is well suitable for implementing on the surveillance and obstacle detection systems.