Nonlinear identification and characterization of structural joints based on vibration transmissibility

In order to investigate the nonlinear characteristics of structural joint,the experimental setup with a jointed mass system is established for dynamic characterization analysis and vibration prediction,and a corresponding nonlinearity identification method is studied.First,the sine-sweep vibration test with different baseexcitation levels areapplied to the structural joint system to study the dominant modal of mass rigid motion.Then,based on t e harmonic balance method principle,t e measured vibration transmissibilities a e utilized for nonlinearity identification using different excitation levels.Experimental results show that nonlinear spring and damping force can be represented by a polynomial order approximation.The identified nonlinear stiffness and damping force can predict the system’s response,and they can reveal t e shifts of resonant frequency or damping due to discontinuity of contact mechanisms within a certain range.

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.

Sufficient variable selection of high dimensional nonparametric nonlinear systems based on Fourier spectrum of density-weighted derivative

The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables.For a high dimensional nonparametric nonlinear system,however,identifying whether a variable contributes or not is not easy.Therefore,based on the Fourier spectrum of densityweighted derivative,one novel variable selection approach is developed,which does not suffer from the dimensionality curse and improves the identification accuracy.Furthermore,a necessary and sufficient condition for testing a variable whether it contributes or not is provided.The proposed approach does not require strong assumptions on the distribution,such as elliptical distribution.The simulation study verifies the effectiveness of the novel variable selection algorithm.

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 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 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.

Nonlinear identification of electro-magnetic force model

Conventional attractive magnetic force models (proportional to the coil current squared and inversely proportional to the gap squared) cannot simulate the nonlinear responses of magnetic bearings in the presence of electromagnetic losses,flux leakage or saturation of iron.In this paper,based on results from an experimental set-up designed to study magnetic force,a novel parametric model is presented in the form of a nonlinear polynomial with unknown coefficients.The parameters of the proposed model are identified using the weighted residual method.Validations of the model identified were performed by comparing the results in time and frequency domains.The results show a good correlation between experiments and numerical simulations.

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.

Data-based model free hysteresis identification for a nonlinear structure

In the last two decades, the damage detection for civil engineering structures has been widely treated as a modal analysis problem and most of the currently available vibration-based system identification approaches are based on modal parameters, namely the natural frequencies, mode shapes and damping ratios, and/or their derivations, which are suitable for linear systems. Nonlinearity is generic in engineering structures. For example, the initiation and development of cracks in civil engineering structures as typical structural damages are nonlinear process. One of the major challenges in damage detection, early warning and damage prognosis is to obtain reasonably accurate identification of nonlinear performance such as hysteresis which is the direct indicator of damage initiation and development under dynamic excitations. In this study, a general data-based identification approach for hysteretic performance in form of nonlinear restoring force using structural dynamic responses and complete and incomplete excitation measurement time series was proposed and validated with a 4-story frame structure equipped with smart devices of magneto-theological （MR） damper to simulate nonlinear performance. Firstly, as an optimization method, the least-squares technique was employed to identify the system matrices of an equivalent linear system of the nonlinear structure model basing on the exci- tation force and the corresponding vibration measurements with impact test when complete and incomplete excitations; and secondly, the nonlinear restoring force of the structure was identified and compared with the test measurements fi- nally. Results show that the proposed data-based approach is capable of identifying the nonlinear behavior of engineering structures and can be employed to evaluate the damage initiation and development of different structure under dynamic loads.

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 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.

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.

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.

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.