Nonlinear System Identification with Unknown Piecewise Time-Varying Delay

Identification of nonlinear systems with unknown piecewise time-varying delay is concerned in this paper.Multiple auto regressive exogenous(ARX) models are identified at different process operating points,and the complete dynamics of the nonlinear system is represented by using a combination of a normalized exponential function as the probability density function with each of the local models.The parameters of the local ARX models and the exponential functions as well as the unknown piecewise time-varying delays are estimated simultaneously under the framework of the expectation maximization(EM) algorithm.A simulation example is applied to demonstrating the proposed identification method.

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.

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.

Nonlinear Dynamic System Identification of ARX Model for Speech Signal Identification

System Identification becomes very crucial in the field of nonlinear and dynamic systems or practical systems.As most practical systems don’t have prior information about the system behaviour thus,mathematical modelling is required.The authors have proposed a stacked Bidirectional Long-Short Term Memory(Bi-LSTM)model to handle the problem of nonlinear dynamic system identification in this paper.The proposed model has the ability of faster learning and accurate modelling as it can be trained in both forward and backward directions.The main advantage of Bi-LSTM over other algorithms is that it processes inputs in two ways:one from the past to the future,and the other from the future to the past.In this proposed model a backward-running Long-Short Term Memory(LSTM)can store information from the future along with application of two hidden states together allows for storing information from the past and future at any moment in time.The proposed model is tested with a recorded speech signal to prove its superiority with the performance being evaluated through Mean Square Error(MSE)and Root Means Square Error(RMSE).The RMSE and MSE performances obtained by the proposed model are found to be 0.0218 and 0.0162 respectively for 500 Epochs.The comparison of results and further analysis illustrates that the proposed model achieves better performance over other models and can obtain higher prediction accuracy along with faster convergence speed.

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.

Nonlinear Model Predictive Control Based on Support Vector Machine with Multi-kernel

Multi-kernel-based support vector machine （SVM） model structure of nonlinear systems and its specific identification method is proposed, which is composed of a SVM with linear kernel function followed in series by a SVM with spline kernel function. With the help of this model, nonlinear model predictive control can be transformed to linear model predictive control, and consequently a unified analytical solution of optimal input of multi-step-ahead predictive control is possible to derive. This algorithm does not require online iterative optimization in order to be suitable for real-time control with less calculation. The simulation results of pH neutralization process and CSTR reactor show the effectiveness and advantages of the presented algorithm.

SVM with Quadratic Polynomial Kernel Function Based Nonlinear Model One-step-ahead Predictive Control

A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.

Support vector machine based nonlinear model multi-step-ahead optimizing predictive control

A support vector machine with guadratic polynomial kernel function based nonlinear model multi-step-ahead optimizing predictive controller was presented. A support vector machine based predictive model was established by black-box identification. And a quadratic objective function with receding horizon was selected to obtain the controller output. By solving a nonlinear optimization problem with equality constraint of model output and boundary constraint of controller output using Nelder-Mead simplex direct search method, a sub-optimal control law was achieved in feature space. The effect of the controller was demonstrated on a recognized benchmark problem and a continuous-stirred tank reactor. The simulation results show that the multi-step-ahead predictive controller can be well applied to nonlinear system, with better performance in following reference trajectory and disturbance-rejection.

Advanced Identification Methods for Industrial Processes with Big Time Delays

This paper presents an advanced method for system identification of industrial processes with big time delays. Identification methods based on neural networks, tree partitioning and wavelet networks are presented and analyzed. The obtained results are compared and the tree partitioning method is selected as most appropriate identification method for the water treatment process. The decision was made based on a thorough analysis on the overall fit between the measured data and the results of the simulated model. At the end, we propose possibilities for further research in this area.

Identification of Suspension Bridge Parameters under Exploitational Conditions

The paper concerns a research into dynamic properties of the steel suspension bridge across Opolska Street in Krakow, Poland. Parameter identification was carried out with the application of the nonlinear system identification method on the basis of system responses to exploitational excitation resulting from pedestrian traffic. In order to verify obtained results, on the basis of the geometrical and material properties of the considered system, the FEM （finite elements model） was created. Created FEM model was updated through the comparison with the model determined by the use of experimental modal analysis method and then applied to analytical evaluation of the considered suspension bridge natural frequencies.

Nonlinear identification of systems with parametric excitation

In this paper, the incremental harmonic balance nonlinear identification (IHBNID) is presented for modelling and parametric identification of nonlinear systems. The effects of harmonic balance nonlinear identification (HBNID) and IHBNID are also studied and compared by using numerical simulation. The effectiveness of the IHBNID is verified through the Mathieu-Duffing equation as an example. With the aid of the new method, the derivation procedure of the incremental harmonic balance method is simplified. The system responses can be represented by the Fourier series expansion in complex form. By keeping several lower-order primary harmonic coefficients to be constant, some of the higher-order harmonic coefficients can be self-adaptive in accordance with the residual errors. The results show that the IHBNID is highly efficient for computation, and excels the HBNID in terms of computation accuracy and noise resistance.

Nonlinear system modeling and identification of small helicopter based on genetic algorithm

Purpose–The purpose of this paper is to build nonlinear model of a small rotorcraft-based unmanned aerial vehicles(RUAV),using nonlinear system identification method to estimate the parameters of the model.The nonlinear model will be used in robust control system design and aerodynamic analysis.Design/methodology/approach–The nonlinear model is built based on mechanism theory,aerodynamics and mechanics,which can reflect most dynamics in large flight envelop.Genetic algorithm(GA)and time domain flight data is adopted to estimate unknown parameters of the model.The flight data were collected from a series of fight tests.The identification results were also analyzed and validated.Findings–The nonlinear model of RUAV has better accuracy,the parameters are physical quantities,and having distinctly recognizable values.The GA is suitable for nonlinear system identification.And the results proved the identified model can reflect the dynamic characteristics in extensive area of flight envelop.Research limitations/implications–The GA requires much more computing power,to identify 12 unknown parameters with 30 iterations,will takes more than 18 hours of a four cores desktop computer.Because of this is an off-line identification process,and has more accuracy,extra time is acceptable.Originality/value–GA method has significantly increased the accuracy of the model.The previous work of system identification used a ten states linear model,and using PEM identified 23 coefficients.By carefully building the nonlinear model,it has only 21 unknown parameters,but if the model is linearized,it will get a linear model more than 35 states,which shows nonlinear model contain more dynamics than linear model.

Genetic programming-based chaotic time series modeling

This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) algorithm is used for Nonlinear Parameter Estimation (NPE) of dynamic model structures. In addition, GPM integrates the results of Nonlinear Time Series Analysis (NTSA) to adjust the parameters and takes them as the criteria of established models. Experiments showed the effectiveness of such improvements on chaotic time series modeling.

MULTI-RESOLUTION LEAST SQUARES SUPPORT VECTOR MACHINES

The Least Squares Support Vector Machines (LS-SVM) is an improvement to the SVM. Combined the LS-SVM with the Multi-Resolution Analysis (MRA),this letter proposes the Multi-resolution LS-SVM (MLS-SVM).The proposed algorithm has the same theoretical framework as MRA but with better approximation ability.At a fixed scale MLS-SVM is a classical LS-SVM,but MLS-SVM can gradually approximate the target function at different scales.In experiments,the MLS-SVM is used for nonlinear system identification,and achieves better identification accuracy.

Generalized Multiscale RBF Networks and the DCT for Breast Cancer Detection

The use of the multiscale generalized radial basis function(MSRBF)neural networks for image feature extraction and medical image analysis and classification is proposed for the first time in this work.The MSRBF networks hold a simple and flexible architecture that has been successfully used in forecasting and model structure detection of input-output nonlinear systems.In this work instead,MSRBF networks are part of an integrated computer-aided diagnosis(CAD)framework for breast cancer detection,which holds three stages:an input-output model is obtained from the image,followed by a high-level image feature extraction from the model and a classification module aimed at predicting breast cancer.In the first stage,the image data is rendered into a multiple-input-single-output(MISO)system.In order to improve the characterisation,the nonlinear autoregressive with exogenous inputs(NARX)model is introduced to rearrange the available input-output data in a nonlinear way.The forward regression orthogonal least squares(FROLS)algorithm is then used to take advantage of the previous arrangement by solving the system as a model structure detection problem and finding the output layer weights of the NARX-MSRBF network.In the second stage,once the network model is available,the feature extraction takes place by stimulating the input to produce output signals to be compressed by the discrete cosine transform(DCT).In the third stage,we leverage the extracted features by using a clustering algorithm for classification to integrate a CAD system for breast cancer detection.To test the method performance,three different and well-known public image repositories were used:the mini-MIAS and the MMSD for mammography,and the BreaKHis for histopathology images.A comparison exercise was also made between different database partitions to understand the mammogram breast density effect in the performance since there are few remarks in the literature on this factor.Classification results show that the new CAD method reached an accuracy of 93.5%in mini-Mammo graphic image analysis society(mini-MIAS),93.99%in digital database for screening mammography(DDSM)and 86.7%in the BreaKHis.We found that the MSRBF networks are able to build tailored and precise image models and,combined with the DCT,to extract high-quality features from both black and white and coloured images.