Reproducing wavelet kernel method in nonlinear system identification

By combining the wavelet decomposition with kernel method, a practical approach of universal multiscale wavelet kernels constructed in reproducing kernel Hilbert space （RKHS） is discussed, and an identification scheme using wavelet support vector machines （WSVM） estimator is proposed for nordinear dynamic systems. The good approximating properties of wavelet kernel function enhance the generalization ability of the proposed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.

Improved System Identification Approach Using Wavelet Networks

A new approach is proposed to improve the general identification algor ithm of multidimensional systems using wavelet networks. The general algorithm i nvolves mapping vector input into its norm to avoid problem of dimensionality in construction multidimensional wavelet basis functions. Thus, the basis function s are spherically symmetric without direction selectivity. In order to restore t he direction selectivity, the improved approach weights the input variables befo r e mapping it into a scalar form. The weights can be obtained using universal opt imization algorithms. Generally, only local optimal weights are obtained. Even s o, performance of identification can be improved.

An Improved Differential Evolution Trained Neural Network Scheme for Nonlinear System Identification

This paper presents an improved nonlinear system identification scheme using di？erential evolution （DE）, neural network （NN） and Levenberg Marquardt algorithm （LM）. With a view to achieve better convergence of NN weights optimization during the training, the DE and LM are used in a combined framework to train the NN. We present the convergence analysis of the DE and demonstrate the efficacy of the proposed improved system identification algorithm by exploiting the combined DE and LM training of the NN and suitably implementing it together with other system identification methods, namely NN and DE＋NN on a number of examples including a practical case study. The identification results obtained through a series of simulation studies of these methods on different nonlinear systems demonstrate that the proposed DE and LM trained NN approach to nonlinear system identification can yield better identification results in terms of time of convergence and less identification error.

An Improved SPSA Algorithm for System Identification Using Fuzzy Rules for Training Neural Networks

Simultaneous perturbation stochastic approximation （SPSA） belongs to the class of gradient-free optimization methods that extract gradient information from successive objective function evaluation. This paper describes an improved SPSA algorithm, which entails fuzzy adaptive gain sequences, gradient smoothing, and a step rejection procedure to enhance convergence and stability. The proposed fuzzy adaptive simultaneous perturbation approximation （FASPA） algorithm is particularly well suited to problems involving a large number of parameters such as those encountered in nonlinear system identification using neural networks （NNs）. Accordingly, a multilayer perceptron （MLP） network with popular training algorithms was used to predicate the system response. We found that an MLP trained by FASPSA had the desired accuracy that was comparable to results obtained by traditional system identification algorithms. Simulation results for typical nonlinear systems demonstrate that the proposed NN architecture trained with FASPSA yields improved system identification as measured by reduced time of convergence and a smaller identification error.

Non-linear Chemical Process Modelling and Application in Epichlorhydrine Production Plant Using Wavelet Networks

A type of wavelet neural network, in which the scale function isadopted only, is proposed in this paper for non-linear dynamicprocess modelling. Its network size is decreased significantly andthe weight coefficients can be estimated by a linear algorithm. Thewavelet neural network holds some advantages superior to other typesof neural networks. First, its network structure is easy to specifybased on its theoretical analysis and intuition. Secondly, networktraining does not rely on stochastic gradient type techniques andavoids the problem of poor convergence or undesirable local minima.

Identification and Control of Dynamical Systems Using Modified Neural Networks

Aim To study the identification and control of nonlinear systems using neural networks. Methods A new type of neural network in which the dynamical error feedback is used to modify the inputs of the network was employed to reduce the inherent network approximation error. Results A new identification model constructed by the proposed network and stable filters was derived for continuous time nonlinear systems, and a stable adaptive control scheme based on the proposed networks was developed. Conclusion Theory and simulation results show that the modified neural network is feasible to control a class of nonlinear systems.

IDENTIFICATION OF NONLINEAR TIME VARYING SYSTEM USING FEEDFORWARD NEURAL NETWORKS

As it is well known,it is difficult to identify a nonlinear time varying system using traditional identification approaches,especially under unknown nonlinear function.Neural networks have recently emerged as a successful tool in the area of identification and control of time invariant nonlinear systems.However,it is still difficult to apply them to complicated time varying system identification.In this paper we present a learning algorithm for identification of the nonlinear time varying system using feedforward neural networks.The main idea of this approach is that we regard the weights of the network as a state of a time varying system,then use a Kalman filter to estimate the state.Thus the network implements nonlinear and time varying mapping.We derived both the global and local learning algorithms.Simulation results demonstrate the effectiveness of this approach.

Nonlinear Time-Varying Systems Identification Using Basis Sequence Expansions Combined with Neural Networks

A new method for identifying nonlinear time varying systems with unknown structure is presented. The method extends the application area of basis sequence identification. The essential idea is to utilize the learning and nonlinear approximating ability of neural networks to model the non linearity of the system, characterize time varying dynamics of the system by the time varying parametric vector of the network, then the parametric vector of the network is approximated by a weighted sum of known basis sequences. Because of black box modeling ability of neural networks, the presented method can identify nonlinear time varying systems with unknown structure. In order to improve the real time capability of the algorithm, the neural network is trained by a simple fast learning algorithm based on local least squares presented by the authors. The effectiveness and the performance of the method are demonstrated by some simulation results.

Efficient Authentication System Using Wavelet Embeddings of Otoacoustic Emission Signals

Biometrics,which has become integrated with our daily lives,could fall prey to falsification attacks,leading to security concerns.In our paper,we use Transient Evoked Otoacoustic Emissions(TEOAE)that are generated by the human cochlea in response to an external sound stimulus,as a biometric modality.TEOAE are robust to falsification attacks,as the uniqueness of an individual’s inner ear cannot be impersonated.In this study,we use both the raw 1D TEOAE signals,as well as the 2D time-frequency representation of the signal using Continuous Wavelet Transform(CWT).We use 1D and 2D Convolutional Neural Networks(CNN)for the former and latter,respectively,to derive the feature maps.The corresponding lower-dimensional feature maps are obtained using principal component analysis,which is then used as features to build classifiers using machine learning techniques for the task of person identification.T-SNE plots of these feature maps show that they discriminate well among the subjects.Among the various architectures explored,we achieve a best-performing accuracy of 98.95%and 100%using the feature maps of the 1D-CNN and 2D-CNN,respectively,with the latter performance being an improvement over all the earlier works.This performance makes the TEOAE based person identification systems deployable in real-world situations,along with the added advantage of robustness to falsification attacks.

NONLINEAR DYNAMIC SYSTEM MODELING USING RECURRENT WAVELET NETWORK

A recurrent wavelet network for the dynamic system nonparametric modeling is proposed in this paper. It is noted that the suitable recurrent units are introduced so that the dynamics of the wavelet network has been greatly improved. The recurrent backpropagation identification algorithm is also given. The simulation results show that regress system model with large-dimension can be better constructed and the useful guidelines for initialization of the network parameter are also provided with recurrent wavelet network identification.

Nonlinear Systems Identification via an Input-Output Model Based on a Feedforward Neural Network

This paper develops a feedforward neural network based input output model for a general unknown nonlinear dynamic system identification when only the inputs and outputs are accessible observations. In the developed model, the size of the input space is directly related to the system order. By monitoring the identification error characteristic curve, we are able to determine the system order and subsequently an appropriate network structure for systems identification. Simulation results are promising and show that generic nonlinear systems can be identified, different cases of the same system can also be discriminated by our model.

Intelligent risk identification of gas drilling based on nonlinear classification network

During the transient process of gas drilling conditions,the monitoring data often has obvious nonlinear fluctuation features,which leads to large classification errors and time delays in the commonly used intelligent classification models.Combined with the structural features of data samples obtained from monitoring while drilling,this paper uses convolution algorithm to extract the correlation features of multiple monitoring while drilling parameters changing with time,and applies RBF network with nonlinear classification ability to classify the features.In the training process,the loss function component based on distance mean square error is used to effectively adjust the best clustering center in RBF.Many field applications show that,the recognition accuracy of the above nonlinear classification network model for gas production,water production and drill sticking is 97.32%,95.25%and 93.78%.Compared with the traditional convolutional neural network(CNN)model,the network structure not only improves the classification accuracy of conditions in the transition stage of conditions,but also greatly advances the time points of risk identification,especially for the three common risk identification points of gas production,water production and drill sticking,which are advanced by 56,16 and 8 s.It has won valuable time for the site to take correct risk disposal measures in time,and fully demonstrated the applicability of nonlinear classification neural network in oil and gas field exploration and development.

Modelling missile motion system using neural networks

The models of noallnear systems are idendried by recmeive pedctive ermrs(RPE) methed based on thelayered neural networks. To improve the identification precision, gain callcient and arentUm factor are itheucedinto the algorithm for the data are dids by noses and vny suddnly. this lerthm is applied to the twcmedeiling of rolling and pitchng angles of ndssiles. Simulation results shoW tha the proposed algurithm is sultable forthe modelling of nodrinear systems.

STUDY ON PREDICTION METHODS FOR DYNAMIC SYSTEMS OF NONLINEAR CHAOTIC TIME SERIES＊

The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions. By combining neural networks and wavelet theories, the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given. Based on wavelet networks, a new method for parameter identification was suggested, which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series. Through pre-treatment and comparison of results before and after the treatment, several useful conclusions are reached: High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.

Nonlinear Identification and Control of Laser Welding Based on RBF Neural Networks

A laser beam is a heat source with a high energy density;this technol-ogy has been rapidly developed and applied in thefield of welding owing to its potential advantages,and supplements traditional welding techniques.An in-depth analysis of its operating process could establish a good foundation for its application in China.It is widely understood that the welding process is a highly nonlinear and multi-variable coupling process;it comprises a significant number of complex processes with random uncertain factors.Because of their nonlinear mapping and self-learning characteristics,artificial neural networks(ANNs)have certain advantages in comparison to traditional methods in thefield of welding.Laser welding is a nonlinear dynamic process;these processes still pose a major challenge in thefield of control.Therefore,establishing a stable model is a pre-requisite for achieving accurate control.In this study,the identification and con-trol of radial basis function neural networks in laser welding processes and self-tuning PID control methods are proposed to improve weld quality.Using a MATLAB simulation,it is shown that the proposed method can obtain a good description of the level of nonlinear dynamic control,and that the algorithm iden-tification accuracy is high,practical,and effective.Using this method,the weld width quickly reaches the expected value and the system remains stable,with good robustness.Further,it ensures the stability and dynamic performance of the welding process and improves weld quality.

Identification of Hammerstein Model Using Hybrid Neural Networks

The identification problem of Hammerstein model with extension to the multi input multi output (MIMO) case is studied. The proposed identification method uses a hybrid neural network (HNN) which consists of a multi layer feed forward neural network (MFNN) in cascade with a linear neural network (LNN). A unified back propagation (BP) algorithm is proposed to estimate the weights and the biases of the MFNN and the LNN simultaneously. Numerical examples are provided to show the efficiency of the proposed method.

Identification of Artificial Neural Network Models for Three-Dimensional Simulation of a Vibration-Acoustic Dynamic System

Industrial noise can be successfully mitigated with the combined use of passive and Active Noise Control (ANC) strategies. In a noisy area, a practical solution for noise attenuation may include both the use of baffles and ANC. When the operator is required to stay in movement in a delimited spatial area, conventional ANC is usually not able to adequately cancel the noise over the whole area. New control strategies need to be devised to achieve acceptable spatial coverage. A three-dimensional actuator model is proposed in this paper. Active Noise Control (ANC) usually requires a feedback noise measurement for the proper response of the loop controller. In some situations, especially where the real-time tridimensional positioning of a feedback transducer is unfeasible, the availability of a 3D precise noise level estimator is indispensable. In our previous works [1,2], using a vibrating signal of the primary source of noise as an input reference for spatial noise level prediction proved to be a very good choice. Another interesting aspect observed in those previous works was the need for a variable-structure linear model, which is equivalent to a sort of a nonlinear model, with unknown analytical equivalence until now. To overcome this in this paper we propose a model structure based on an Artificial Neural Network (ANN) as a nonlinear black-box model to capture the dynamic nonlinear behaveior of the investigated process. This can be used in a future closed loop noise cancelling strategy. We devise an ANN architecture and a corresponding training methodology to cope with the problem, and a MISO (Multi-Input Single-Output) model structure is used in the identification of the system dynamics. A metric is established to compare the obtained results with other works elsewhere. The results show that the obtained model is consistent and it adequately describes the main dynamics of the studied phenomenon, showing that the MISO approach using an ANN is appropriate for the simulation of the investigated process. A clear conclusion is reached highlighting the promising results obtained using this kind of modeling for ANC.

Wavelet neural network based fault diagnosis in nonlinear analog circuits

The theories of diagnosing nonlinear analog circuits by means of the transient response testing are studled. Wavelet analysis is made to extract the transient response signature of nonlinear circuits and compress the signature dada. The best wavelet function is selected based on the between-category total scatter of signature. The fault dictionary of nonlinear circuits is constructed based on improved back-propagation（BP） neural network. Experimental results demonstrate that the method proposed has high diagnostic sensitivity and fast fault identification and deducibility.

A novel internet traffic identification approach using wavelet packet decomposition and neural network

Internet traffic classification plays an important role in network management, and many approaches have been proposed to classify different kinds of internet traffics. A novel approach was proposed to classify network applications by optimized back-propagation (BP) neural network. Particle swarm optimization (PSO) algorithm was used to optimize the BP neural network. And in order to increase the identification performance, wavelet packet decomposition (WPD) was used to extract several hidden features from the time-frequency information of network traffic. The experimental results show that the average classification accuracy of various network applications can reach 97%. Moreover, this approach optimized by BP neural network takes 50% of the training time compared with the traditional neural network.

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.