Nonlinear Dynamic System Identification Based on Multiobjectively Selected RBF Networks

Teaching Aids for Modeling and Control of Hybrid Systems (CAMCHS)

Nonlinear dynamic systems are characterized with uncertainties in terms of structure and parameters. These uncertainties cannot be described by deterministic models. The modelling and identification of nonlinear dynamic systems through the measured experimental data is a problem in engineering and technical processes. Therefore, field of system identification have become an important area of research. Fuzzy technology is an effective tool for dealing with complex nonlinear processes that are characterized with uncertain factors. In this paper, a novel approach based on Local Linear method learning in dynamical filter weights neurons for the identification of non-linear dynamic systems is presented. The fuzzy wavelet neural network combines wavelet theory with fuzzy logic and neural networks. Learning fuzzy rules and parameter update in fuzzy wavelet neural network is based on gradient decent method. The proposed approach is said to be Fuzzy Local Linear Wavelet Neural Network based model. It has been explained through examples. The structure is tested for the identification with both wavelet neural network and Fuzzy Local Linear Wavelet Neural Network that shows the comparative performance.KeywordsSystem IdentificationNon-linear SystemWavelet Neural NetworkFuzzy Wavelet Neural NetworkLocal Linear Wavelet Neural NetworkFuzzy Local Linear Wavelet Neural Network

A method for identifying nonlinear dynamic systems with noise is proposed by using probabilistic universal learning networks (PrULNs). PrULNs are extensions of universal learning networks (ULNs). ULNs form a superset of neural networks and were proposed to provide a universal framework for modeling and control of nonlinear large-scale complex systems. But the ULN does not provide any stochastic characteristics of the signals propagating through it. The PrULNs are equipped with machinery to calculate stochastic properties of signals and to train network parameters so that the signals behave with the pre-specified stochastic properties. On the other hand it is generally recognized that there exists an overfitting problem when identification of nonlinear dynamic systems with noise is done by neural networks. In this paper, it is shown from simulation results of identification of a nonlinear robot dynamics that PrULNs are useful for avoiding the overfitting.

This article presents a theoretical framework for the identification of nonlinear dynamic MISO systems with orthonormal base function models on fundamental basics of the Volterra theory. In the past the Volterra theory was used for the identification of nonlinear dynamic SISO systems (e.g. Hammerstein and Wiener models). In principle it is possible to extend these approaches to systems with more than one input (i.e. MISO systems). In former times this failed due to a lack of computational performance. In this paper an approach is presented which allows the identification of arbitrary coupled Hammerstein and Wiener models with multiple inputs. Some fundamental considerations for the identification of MISO systems based on arbitrary coupled Hammerstein models are made and extended to MISO systems based on arbitrary coupled Wiener models. This extended Volterra theory results in equations where the unknown parameters can be separated of the input values in a linear manner. In order to approximate the truncated impulse responses of the linear dynamic systems and to reduce the number of unknown parameters orthonormal base functions (OBFs) are introduced. As an example the proposed identification method is applied to a MISO system based on forward and backward coupled Hammerstein and Wiener models.

This paper compares radial basis function networks for identification of nonlinear dynamic systems with classical methods derived from the Volterra series. The performance of these different approaches, such as Hammerstein, Wiener and NDE models, is analysed. Since the centres and variances of the Gaussian radial basis functions will be fixed before learning and only the weights are learned, a linear optimization problem arises. Therefore training the network and parameter estimation becomes comparable in computational effort. It is shown that the classical methods can compete or even perform better than the neural network, if the assumptions for the structure are valid. However, in practical applications when the structure is not known the radial basis function network performs much better than the classical methods.

The paper demonstrates that radial basis function network (RBFN) with adaptive centers and width can be used effectively for identification of nonlinear dynamic system. The proposed RBFN is trained by hybrid learning algorithm, which uses conjugate gradient optimization algorithm to obtain the center and width of each radial basis function and the least squares method to obtain the weights. To avoid capturing a local optimum, regularization error energy function is used and the centers of basis functions are initialized using a fuzzy C-means clustering method. Simulation results reveal that the identification schemes based on RBFN gives considerably better performance and show faster learning in comparison to previous methods

In this study, nonlinear dynamic systems are identified by using artificial bee colony (ABC) algorithm and adaptive neuro fuzzy inference system (ANFIS). ABC algorithm is used in training and updating of ANFIS. The most appropriate model is formed by optimizing the antecedent and conclusion parameters that are found in the structure of ANFIS. The dynamic systems that consist of one input and one output (SISO) are used for the identification of nonlinear dynamic systems. The obtained results are compared with fuzzy neural network, neural network and ANFIS-based methods such as RSONFIN, DFNN, RSEFNN-LF, WRFNN and RFNN. The simulation results show that the proposed method is successful in the identification of considered nonlinear dynamic systems.

In this paper, the use of radial basis function network (RBFN) for simultaneous online identification and indirect adaptive control of nonlinear dynamical systems is demonstrated. The motivation of using RBFN comes from the simplicity of its structure and simpler mathematical formulation, which gives it an advantage over multi-layer feed-forward neural network (MLFFNN). Since most processes are nonlinear, the use of conventional proportional-integral-derivative controller is not useful. Most of the time plant’s dynamics information is not available. This creates another limitation on the use of conventional control techniques, which works only if plant’s dynamics information is available. The proposed controller is tested for parameter variations and disturbance effects. Simulation results showed that RBFN is able to capture the unknown dynamics as well as simultaneously able to adaptively control the plant. It is also found to compensate the effects of parameter variations and disturbances. The comparative analysis is also done with MLFFNN in each simulation example, and it is found that performance of RBFN is better than that of MLFFNN.

This paper covers the state of the art in nonlinear dynamical system identification using artificial neural networks (ANN). The main approaches in the last two decades are presented in unified framework. ANN has unique characteristics, which enable them to model nonlinear dynamical systems. The main problems with the choice of ANN model structure are considered and commonly used identification schemes are proposed. A procedure for derivation of parameter estimation law using Lyapunov synthesis approach, which guarantees stability and convergence of the overall identification scheme, is presented

A procedure based on the use of artificial neural networks for the identification of nonlinear dynamic systems is developed and applied to the damped Duffing oscillator under deterministic excitation. The “generalization” ability of neural networks is invoked to predict the response of the same nonlinear oscillator under stochastic excitations of differing magnitude. The analogy between the neural network approach and a qualitatively similar nonparametric identification technique previously developed by the authors is illustrated. Some of the computational aspects of identification by neural networks, as well as their fault-tolerant nature, are discussed. It is shown that neural networks provide high-fidelity mathematical models of structure-unknown nonlinear systems encountered in the applied mechanics field.

Diagonal recurrent neural network based identification of nonlinear dynamical systems with Lyapunov stability based adaptive learning rates

This paper presents developed engineering software tools used for nonparametric identification of nonlinear dynamical systems based on Volterra models. The polyharmonic test sequences with different amplitudes are used for test procedures in frequency domain. The wavelets application allowed enlarging computational stability of the identification method for measurement noises filtering of received responses and characteristics of the system being identified. The methodology proposed in pervious works and developed software tools applied for construction communication channel models of different orders.

The identification and modeling of linear and nonlinear dynamic systems through the use of measured experimental data is a problem of considerable importance in engineering. Among the identification methods, the artificial neural network is a newly developed technique. Due to its attributes, such as parallelism, adaptability, robustness, and the inherent ability to handle nonlinearity, artificial neural networks have shown great promise in function mapping, pattern recognition, image processing, and so on. However, dynamic function mapping, including the structural dynamic model identification, is still a challenging topic in neural network applications. A neural network approach for structural dynamic model identification is presented in this paper. The neural network is trained, tested, and verified by using the responses recorded in a real apartment building during earthquakes. The results show that the dynamic behaviors of the building can be very well modeled by the trained neural network. The results also indicate the great potential of using neural networks in structural dynamic model identification.

An identification method of nonlinear dynamic system is studied in this paper. First, suppose that the original nonlinear dynamic system is described by Hammerstein model. Then, an intermediate model is generated. Next, Parameters of the intermediate model are obtained using a Bacterial Chemotaxis Optimization (BCO) approach. Finally, through the relationships of the parameters of intermediate model and those of Hammerstein model, we derive the parameters of the system. Consequently, the original nonlinear dynamic system is identified. The feasibility and efficiency of the presented algorithm are demonstrated using numerical simulations.

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.