Approximation to NLAR(p) with Wavelet Neural Networks

Recently, wavelet neural networks have become a popular tool for non-linear functional approximation. Wavelet neural networks, which basis functions are orthonormal scalling functions, are more suitable in approximating to function. Based on it, approximating to NLAR(p) with wavelet neural networks is studied.

Discussion of stability in a class of models on recurrent wavelet neural networks

Based on wavelet neural networks （WNNs） and recurrent neural networks （RNNs）, a class of models on recurrent wavelet neural networks （RWNNs） is proposed. The new networks possess the advantages of WNNs and RNNs. In this paper, asymptotic stability of RWNNs is researched.according to the Lyapunov theorem, and some theorems and formulae are given. The simulation results show the excellent performance of the networks in nonlinear dynamic system recognition.

Stock Price Prediction Using Predictive Error Compensation Wavelet Neural Networks

:Machine Learning(ML)algorithms have been widely used for financial time series prediction and trading through bots.In this work,we propose a Predictive Error Compensated Wavelet Neural Network(PEC-WNN)ML model that improves the prediction of next day closing prices.In the proposed model we use multiple neural networks where the first one uses the closing stock prices from multiple-scale time-domain inputs.An additional network is used for error estimation to compensate and reduce the prediction error of the main network instead of using recurrence.The performance of the proposed model is evaluated using six different stock data samples in the New York stock exchange.The results have demonstrated significant improvement in forecasting accuracy in all cases when the second network is used in accordance with the first one by adding the outputs.The RMSE error is 33%improved when the proposed PEC-WNN model is used compared to the Long ShortTerm Memory(LSTM)model.Furthermore,through the analysis of training mechanisms,we found that using the updated training the performance of the proposed model is improved.The contribution of this study is the applicability of simultaneously different time frames as inputs.Cascading the predictive error compensation not only reduces the error rate but also helps in avoiding overfitting problems.

Wavelet Neural Networks for Adaptive Equalization by Using the Orthogonal Least Square Algorithm

Equalizers are widely used in digital communication systems for corrupted or time varying channels. To overcome performance decline for noisy and nonlinear channels, many kinds of neural network models have been used in nonlinear equalization. In this paper, we propose a new nonlinear channel equalization, which is structured by wavelet neural networks. The orthogonal least square algorithm is applied to update the weighting matrix of wavelet networks to form a more compact wavelet basis unit, thus obtaining good equalization performance. The experimental results show that performance of the proposed equalizer based on wavelet networks can significantly improve the neural modeling accuracy and outperform conventional neural network equalization in signal to noise ratio and channel non-linearity.

Establishment of a Fault Prognosis Model Using Wavelet Neural Networks and Its Engineering Application

Fault diagnosis is confronted with two problems; how to '' measure'' the growthof a fault and how to predict the remaining useful lifetime of such a failing component or machine.This paper attempts to solve these two problems by proposing a model of fault prognosis usingwavelet basis neural network. Gaussian radial basis functions and Mexican hat wavelet frames areused as scaling functions and wavelets, respectively. The centers of the basis functions arecalculated using a dyadic expansion scheme and a k-means clustering algorithm.

Combining unscented Kalman filter and wavelet neural network for anti-slug

The stability of the subsea oil and gas production system is heavily influenced by slug flow. One successful method of managing slug flow is to use top valve control based on subsea pipeline pressure. However, the complexity of production makes it difficult to measure the pressure of subsea pipelines, and measured values are not always accessible in real-time. The research introduces a technique for integrating Unscented Kalman Filter (UKF) and Wavelet Neural Network (WNN) to estimate the state of subsea pipeline pressure using historical data and a state model. The proposed method treats multiphase flow transport as a nonlinear model, with a dynamic WNN serving as the state observer. To achieve real-time state estimation, the WNN is included into the UKF algorithm to create a WNN-based UKF state equation. Integrate WNN and UKF in a novel way to predict system state accurately. The simulated results show that the approach can efficiently predict the inlet pressure and manage the slug flow in real-time using the riser's top pressure, outlet flow and valve opening. This method of estimate can significantly increase the control effect.

Optimal Wavelet Neural Network-Based Intrusion Detection in Internet of Things Environment

As the Internet of Things(IoT)endures to develop,a huge count of data has been created.An IoT platform is rather sensitive to security challenges as individual data can be leaked,or sensor data could be used to cause accidents.As typical intrusion detection system(IDS)studies can be frequently designed for working well on databases,it can be unknown if they intend to work well in altering network environments.Machine learning(ML)techniques are depicted to have a higher capacity at assisting mitigate an attack on IoT device and another edge system with reasonable accuracy.This article introduces a new Bird Swarm Algorithm with Wavelet Neural Network for Intrusion Detection(BSAWNN-ID)in the IoT platform.The main intention of the BSAWNN-ID algorithm lies in detecting and classifying intrusions in the IoT platform.The BSAWNN-ID technique primarily designs a feature subset selection using the coyote optimization algorithm(FSS-COA)to attain this.Next,to detect intrusions,the WNN model is utilized.At last,theWNNparameters are optimally modified by the use of BSA.Awidespread experiment is performed to depict the better performance of the BSAWNNID technique.The resultant values indicated the better performance of the BSAWNN-ID technique over other models,with an accuracy of 99.64%on the UNSW-NB15 dataset.

SOC estimation of lithium-ion power battery for HEV based on advanced wavelet neural network

In order to improve the estimation accuracy of the battery＇s state of charge（SOC） for the hybrid electric vehicle（HEV）,the SOC estimation algorithm based on advanced wavelet neural network（WNN） is presented.Based on advanced WNN,the SOC estimation model of a lithium-ion power battery for the HEV is first established.Then,the convergence of the advanced WNN algorithm is proved by mathematical deduction.Finally,using an adequate data sample of various charging and discharging of HEV batteries,the neural network is trained.The simulation results indicate that the proposed algorithm can effectively decrease the estimation errors of the lithium-ion power battery SOC from the range of ±8% to ±1.5%,compared with the traditional SOC estimation methods.

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.

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.

Time series prediction using wavelet process neural network

In the real world, the inputs of many complicated systems are time-varying functions or processes. In order to predict the outputs of these systems with high speed and accuracy, this paper proposes a time series prediction model based on the wavelet process neural network, and develops the corresponding learning algorithm based on the expansion of the orthogonal basis functions. The effectiveness of the proposed time series prediction model and its learning algorithm is proved by the Macke-Glass time series prediction, and the comparative prediction results indicate that the proposed time series prediction model based on the wavelet process neural network seems to perform well and appears suitable for using as a good tool to predict the highly complex nonlinear time series.

Dynamic prediction of gas emission based on wavelet neural network toolbox

This paper presents a method for dynamically predicting gas emission quantity based on the wavelet neural network （WNN） toolbox. Such a method is able to predict the gas emission quantity in adjacent subsequent time intervals through training the WNN with even time-interval samples. The method builds successive new model with the width of sliding window remaining invariable so as to obtain a dynamic prediction method for gas emission quantity. Furthermore, the method performs prediction by a self-developed WNN toolbox. Experiments indicate that such a model can overcome the deficiencies of the traditional static prediction model and can fully make use of the feature extraction capability of wavelet base function to reflect the geological feature of gas emission quantity dynamically. The method is characterized by simplicity, flexibility, small data scale, fast convergence rate and high prediction precision. In addition, the method is also characterized by certainty and repeatability of the predicted results. The effectiveness of this method is confirmed by simulation results. Therefore, this method will exert practical significance on promoting the application of WNN.

Adaptive control of machining process based on extended entropy square error and wavelet neural network

Combining information entropy and wavelet analysis with neural network,an adaptive control system and an adaptive control algorithm are presented for machining process based on extended entropy square error(EESE)and wavelet neural network(WNN).Extended entropy square error function is defined and its availability is proved theoretically.Replacing the mean square error criterion of BP algorithm with the EESE criterion,the proposed system is then applied to the on-line control of the cutting force with variable cutting parameters by searching adaptively wavelet base function and self adjusting scaling parameter,translating parameter of the wavelet and neural network weights.Simulation results show that the designed system is of fast response,non-overshoot and it is more effective than the conventional adaptive control of machining process based on the neural network.The suggested algorithm can adaptively adjust the feed rate on-line till achieving a constant cutting force approaching the reference force in varied cutting conditions,thus improving the machining efficiency and protecting the tool.

Backstepping sliding mode control with self recurrent wavelet neural network observer for a novel coaxial twelve-rotor UAV

The robust attitude control for a novel coaxial twelve-rotor UAV which has much greater payload capacity,higher drive capability and damage tolerance than a quad-rotor UAV is studied. Firstly,a dynamical and kinematical model for the coaxial twelve-rotor UAV is designed. Considering model uncertainties and external disturbances,a robust backstepping sliding mode control( BSMC) with self recurrent wavelet neural network( SRWNN) method is proposed as the attitude controller for the coaxial twelve-rotor. A combinative algorithm of backstepping control and sliding mode control has simplified design procedures with much stronger robustness benefiting from advantages of both controllers. SRWNN as the uncertainty observer is able to estimate the lumped uncertainties effectively.Then the uniformly ultimate stability of the twelve-rotor system is proved by Lyapunov stability theorem. Finally,the validity of the proposed robust control method adopted in the twelve-rotor UAV under model uncertainties and external disturbances are demonstrated via numerical simulations and twelve-rotor prototype experiments.

Self-correcting wavelet neural network control of continuous rotary electro-hydraulic servo motor

In allusion to the problem of friction,leakage,vibration and noise existing in continuous rotary motor electro-hydraulic servo system,highly nonlinearity and uncertainties affecting the system performance,based on the transfer function of electro-hydraulic servo system,a kind of Pol-Ind friction model is proposed.The parameters of Pol-Ind friction model are identified and the accurate mathematical model of friction torque is obtained by experiment.The self-correcting wavelet neural network(WNN)controller is proposed,and Adam optimization algorithm is used to perform gradient optimization on scale factor and displacement factor in wavelet basis function,so as to improve the speed and precision of parameter optimization.Through comparative simulation analysis,it is clearly that the self-correcting WNN controller can effectively improve the frequency response and tracking accuracy of continuous rotary motor electro-hydraulic servo system.

ADAPTIVE FLIGHT CONTROL SYSTEM OF ARMED HELICOPTER USING WAVELET NEURAL NETWORK METHOD

A discussion is devoted to the design of an adaptive flight control system of the armed helicopter using wavelet neural network method. Firstly, the control loop of the attitude angle is designed with a dynamic inversion scheme in a quick loop and a slow loop. respectively. Then, in order to compensate the error caused by dynamic inversion, the adaptive flight control system of the armed helicopter using wavelet neural network method is put forward, so the BP wavelet neural network and the Lyapunov stable wavelet neural network are used to design the helicopter flight control system. Finally, the typical maneuver flight is simulated to demonstrate its validity and effectiveness. Result proves that the wavelet neural network has an engineering practical value and the effect of WNN is good.

A Compensation Controller Based on a Nonlinear Wavelet Neural Network for Continuous Material Processing Operations

Continuous material processing operations like printing and textiles manufacturing are conducted under highly variable conditions due to changes in the environment and/or in the materials being processed.As such,the processing parameters require robust real-time adjustment appropriate to the conditions of a nonlinear system.This paper addresses this issue by presenting a hybrid feedforward-feedback nonlinear model predictive controller for continuous material processing operations.The adaptive feedback control strategy of the controller augments the standard feedforward control to ensure improved robustness and compensation for environmental disturbances and/or parameter uncertainties.Thus,the controller can reduce the need for manual adjustments.The controller applies nonlinear generalized predictive control to generate an adaptive control signal for attaining robust performance.A wavelet-based neural network model is adopted as the prediction model with high prediction precision and time-frequency localization characteristics.Online training is utilized to predict uncertain system dynamics by tuning the wavelet neural network parameters and the controller parameters adaptively.The performance of the controller algorithm is verified by both simulation,and in a real-time practical application involving a single-input single-output double-zone sliver drafting system used in textiles manufacturing.Both the simulation and practical results demonstrate an excellent control performance in terms of the mean thickness and coefficient of variation of output slivers,which verifies the effectiveness of this approach in improving the long-term uniformity of slivers.

Optimization of a crude distillation unit using a combination of wavelet neural network and line-up competition algorithm

The modeling and optimization of an industrial-scale crude distillation unit （CDU） are addressed. The main spec- ifications and base conditions of CDU are taken from a crude oil refinery in Wuhan, China. For modeling of a com- plicated CDU, an improved wavelet neural network （WNN） is presented to model the complicated CDU, in which novel parametric updating laws are developed to precisely capture the characteristics of CDU. To address CDU in an economically optimal manner, an economic optimization algorithm under prescribed constraints is presented. By using a combination of WNN-based optimization model and line-up competition algorithm （LCA）, the supe- rior performance of the proposed approach is verified. Compared with the base operating condition, it is validat- ed that the increments of products including kerosene and diesel are up to 20% at least by increasing less than 5% duties of intermediate coolers such as second pump-around （PA2） and third Dump-around （PA3）.

MOVING TARGETS PATTERN RECOGNITION BASED ON THE WAVELET NEURAL NETWORK

Based on pattern recognition theory and neural network technology, moving objects automatic detection and classification method integrating advanced wavelet analysis are discussed in detail. An algorithm of moving targets pattern recognition on the combination of inter-frame difference and wavelet neural network is presented. The experimental results indicate that the designed BP wavelet network using this algorithm can recognize and classify moving targets rapidly and effectively.

Research on transformer protection based on wavelet neural network and FPGA

The paper expounds importance of the transformer protection and analyzes the magnetizing inrush current produce condition. A comprehensive prevention based on the wavelet neural network methods for identification the magnetizing inrush current is put forward in this paper. Based on a lot of simulations, it can be drawn that sympathetic inrush waveform has no obvious difference with that of the inrush current. According to the characteristics of wavelet neural networks＇ huge computation and high sampling rate, a new method based on FPGA of a high-speed hardware platform is proposed to realise the algorithm. Utilizing technologies of wavelet neural networks and FPGA, the accuracy and real-time data processing speed of the protection device can be more effective. In a word, the research has high theoretical and practical value in the further improvement of transformer protection.