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.

Nonlinear Modeling and Identification of the Electro-hydraulic Control System of an Excavator Arm Using BONL Model

Electro-hydraulic control systems are nonlinear in nature and their mathematic models have unknown parameters. Existing research of modeling and identification of the electro-hydraulic control system is mainly based on theoretical state space model, and the parameters identification is hard due to its demand on internal states measurement. Moreover, there are also some hard-to-model nonlinearities in theoretical model, which needs to be overcome. Modeling and identification of the electro-hydraulic control system of an excavator arm based on block-oriented nonlinear（BONL） models is investigated. The nonlinear state space model of the system is built first, and field tests are carried out to reveal the nonlinear characteristics of the system. Based on the physic insight into the system, three BONL models are adopted to describe the highly nonlinear system. The Hammerstein model is composed of a two-segment polynomial nonlinearity followed by a linear dynamic subsystem. The Hammerstein-Wiener（H-W） model is represented by the Hammerstein model in cascade with another single polynomial nonlinearity. A novel Pseudo-Hammerstein-Wiener（P-H-W） model is developed by replacing the single polynomial of the H-W model by a non-smooth backlash function. The key term separation principle is applied to simplify the BONL models into linear-in-parameters struc^tres. Then, a modified recursive least square algorithm（MRLSA） with iterative estimation of internal variables is developed to identify the all the parameters simultaneously. The identification results demonstrate that the BONL models with two-segment polynomial nonlinearities are able to capture the system behavior, and the P-H-W model has the best prediction accuracy. Comparison experiments show that the velocity prediction error of the P-H-W model is reduced by 14%, 30% and 75% to the H-W model, Hammerstein model, and extended auto-regressive （ARX） model, respectively. This research is helpful in controller design, system monitoring and diagnosis.

Nonlinear Modeling and Identification of Structural Joint by Response Control Vibration Test

Components of mechanical product are assembled by structural joints,such as bolting,riveting,welding,etc.Structural joints introduce nonlinearity to some engineering structures,and the nonlinearity need to be modeled precisely.To meet serious quality requirements,it is necessary to detect and identify nonlinearity of mechanical products for structural optimization.Modal test to acquire a dynamic response has been applied for decades,which provides reliable results for finite element(FE)model updating.Here response control vibration test for identification of nonlinearity is presented.A nonlinear system can be regarded as linearity for particular steady state response,and classical linear analysis tool is applicable to extract modal data for particular response.First,its applicability is illustrated by some numerical simulations.Subsequently,it is implemented on experimental setup with structural joints by shaking table.The stiffness and damping function dependent of relative displacement are fitted to describe its inherent nonlinearity.The spring and damping forces are identified by harmonic balance method(HBM)to predict output response.Based on the identified results,the procedure is recommended that it allows a reliable measurement of nonlinearity with a certain accuracy.

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.

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.

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.

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.

A Local Sparse Screening Identification Algorithm with Applications

Extracting nonlinear governing equations from noisy data is a central challenge in the analysis of complicated nonlinear behaviors.Despite researchers follow the sparse identification nonlinear dynamics algorithm(SINDy)rule to restore nonlinear equations,there also exist obstacles.One is the excessive dependence on empirical parameters,which increases the difficulty of data pre-processing.Another one is the coexistence of multiple coefficient vectors,which causes the optimal solution to be drowned in multiple solutions.The third one is the composition of basic function,which is exclusively applicable to specific equations.In this article,a local sparse screening identification algorithm(LSSI)is proposed to identify nonlinear systems.First,we present the k-neighbor parameter to replace all empirical parameters in data filtering.Second,we combine the mean error screening method with the SINDy algorithm to select the optimal one from multiple solutions.Third,the time variable t is introduced to expand the scope of the SINDy algorithm.Finally,the LSSI algorithm is applied to recover a classic ODE and a bi-stable energy harvester system.The results show that the new algorithm improves the ability of noise immunity and optimal parameters identification provides a desired foundation for nonlinear analyses.

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.

Adaptive robust control of soft bending actuators:an empirical nonlinear model-based approach

Soft robotics,compared with their rigid counterparts,are able to adapt to uncharted environments,are superior in safe human-robot interactions,and have low cost,owing to the native compliance of the soft materials.However,customized complex structures,as well as the nonlinear and viscoelastic soft materials,pose a great challenge to accurate modeling and control of soft robotics,and impose restrictions on further applications.In this study,a unified modeling strategy is proposed to establish a complete dynamic model of the most widely used pneumatic soft bending actuator.First,a novel empirical nonlinear model with parametric and nonlinear uncertainties is identified to describe the nonlinear behaviors of pneumatic soft bending actuators.Second,an inner pressure dynamic model of a pneumatic soft bending actuator is established by introducing a modified valve flow rate model of the unbalanced pneumatic proportional valves.Third,an adaptive robust controller is designed using a backstepping method to handle and update the nonlinear and uncertain system.Finally,the experimental results of comparative trajectory tracking control indicate the validity of the proposed modeling and control method.

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.