Identification Of Nonlinear Models Research Articles

Combination of fractional FLANN filters for solving the Van der Pol-Duffing oscillator

Functional link artificial neural network (FLANN) has received much attention due to its wide applicability. The Van der Pol-Duffing oscillator (VdPDO)-based nonlinear systems, which own complex dynamical behaviors, identification of such nonlinear model is vital. This paper exploits the nonlocality of fractional calculus, aiming to enhance the identification accuracy of the VdPDO-based nonlinear systems. The proposed combined FEM-LMS (CFEM-LMS) algorithm, which is based on the FLANN structure, convexly combines the least mean square (LMS) algorithm and the newly proposed fractional-order error modified LMS (FEM-LMS) algorithm. The CFEM-LMS algorithm has improved performance and can dynamically adapt to the nonlinearity of the system. As an added contribution, a novel mixing parameter adaptation criterion is proposed for performance improvement. Extensive simulation results in the context of VdPDO-based nonlinear system identification demonstrate the superiority of the proposed algorithm as compare to state-of-the-art approaches.

Identification of nonlinear model for rotary high aspect ratio flexible blade using free vibration response

Nonlinear identification of a narrow cantilever blade undergoing free vibration was studied. In the absence of forced excitation and because of general data deficiency of this system, the current identification methods cannot be applied with sufficient accuracy. A new identification approach was introduced in the present study based on nonlinear free vibration decay. Nonlinear free response of the presented system is determined by the coupling of generalized variation iteration and the modified differential transformation methods. The comparisons between the experiments and calculations is highlighted the good accuracy of the identified nonlinear model.

Momentum Least Mean Square Paradigm for the Measurement of Nonlinear CARAR System Parameters

Abstract This study presents a variant of least mean square (LMS) algorithm, i.e., momentum LMS (M-LMS), with faster convergence speed for measuring the system parameter of linear as well as nonlinear control autoregressive autoregressive (CARAR) models. The M-LMS effectively exploits the input/output data by utilizing the previous gradients information in update rule to avoid trapping in local minimum (MNM) and yields better convergence behavior than conventional LMS approach. The speedy convergence of M-LMS is achieved by increasing the proportion of previous gradients but at the cost of little compromise in final steady-state behavior. The correctness of the M-LMS is established by effective optimization of the linear as well as nonlinear CARAR model identification. The robustness of the scheme is verified through accurate measurement of CARAR systems parameters for various noise levels. The statistical analyses based on multiple independent trials through proximity measures in terms of fitness, mean squared error, and Nash Sutcliffe efficiency further validated the superior performance of M-LMS for identification of CARAR models.

On the vanishing and exploding gradient problem in Gated Recurrent Units

Recurrent Neural Networks are applied in areas such as speech recognition, natural language and video processing, and the identification of nonlinear state space models. Conventional Recurrent Neural Networks, e.g. the Elman Network, are hard to train. A more recently developed class of recurrent neural networks, so-called Gated Units, outperform their counterparts on virtually every task. This paper aims to provide additional insights into the differences between RNNs and Gated Units in order to explain the superior perfomance of gated recurrent units. It is argued, that Gated Units are easier to optimize not because they solve the vanishing gradient problem, but because they circumvent the emergence of large local gradients.

Integrated Neural Networks for Nonlinear Continuous-Time System Identification

This letter introduces a novel neural network architecture, called Integrated Neural Network (INN), for direct identification of nonlinear continuous-time dynamical models in state-space representation. The proposed INN is used to approximate the continuous-time state map, and it consists of a feed-forward network followed by an integral block. The unknown parameters are estimated by minimizing a properly constructed dual-objective criterion. The effectiveness of the proposed methodology is assessed against the Cascaded Tanks System benchmark.

On the Initialization of Nonlinear LFR Model Identification with the Best Linear Approximation

Balancing the model complexity and the representation capability towards the process to be captured remains one of the main challenges in nonlinear system identification. One possibility to reduce model complexity is to impose structure on the model representation. To this end, this work considers the linear fractional representation framework. In a linear fractional representation the linear dynamics and the system nonlinearities are modeled by two separate blocks that are interconnected with one another. This results in a structured, yet flexible model structure. Estimating such a model directly from input-output data is not a trivial task as the involved optimization is nonlinear in nature. This paper proposes an initialization scheme for the model parameters based on the best linear approximation of the system and shows that this approach results in high quality models on a set of benchmark data sets.

Linearization in the Large of the Anaerobic Digestion Process Using a Reduced-Order Koopman Operator

The identification of accurate models for the anaerobic digestion process is essential for the characterization of the region that guarantees the conservation of the bacteria population. Traditional techniques involve the identification of nonlinear models based on data from the system. In this paper, we introduce data-driven techniques that allow the characterization of the system’s behavior via the approximation of the Koopman operator with the extended dynamic mode decomposition algorithm. We propose methods to reduce the order and dimension of the representation based on orthogonal polynomials.

Optimal design of excitation signal for identification of nonlinear ship manoeuvring model

An optimal design scheme of excitation signals is presented to determine the training data that provides the maximum dynamic information to improve the stability and accuracy of the identification of ship manoeuvring models. A multi-level pseudo-random sequence is selected as the optimized object for covering the maximum nonlinear dynamic characteristics. The amount of information is quantified by the D-optimality criterion, and the optimal solution is calculated by the ant colony optimization algorithm. Monte Carlo analysis and generalization validation are conducted to evaluate the optimized signals. The superiority of the optimized excitation signal is demonstrated by comparing with the widely used zigzag manoeuvre signal. In the presence of noise interference, the application of the optimized training data reduces the variance of parameter estimation and improves the generalization ability of the identified model, especially for the surge equation.

An Optimization-Based Framework for Nonlinear Model Selection and Identification

This paper proposes an optimization-based framework to determine the type of nonlinear model present and identify its parameters. The objective in this optimization problem is to identify the parameters of a nonlinear model by minimizing the differences between the experimental and analytical responses at the measured coordinates of the nonlinear structure. The application of the method is demonstrated on a clamped beam subjected to a nonlinear electromagnetic force. In the proposed method, the assumption is that the form of nonlinear force is not known. For this reason, one may assume that any nonlinear force can be described using a Taylor series expansion. In this paper, four different possible nonlinear forms are assumed to model the electromagnetic force. The parameters of these four nonlinear models are identified from experimental data obtained from a series of stepped-sine vibration tests with constant acceleration base excitation. It is found that a nonlinear model consisting of linear damping and linear, quadratic, cubic, and fifth order stiffness provides excellent agreement between the predicted responses and the corresponding measured responses. It is also shown that adding a quadratic nonlinear damping does not lead to a significant improvement in the results.

ФУНКЦИОНАЛЬНО-ДИФФЕРЕНЦИАЛЬНЫЕ И ДИФФЕРЕНЦИАЛЬНО-РАЗНОСТНЫЕ МОДЕЛИ СИСТЕМ С АКУСТИЧЕСКОЙ ОБРАТНОЙ СВЯЗЬЮ

The paper reports the investigations of the functional differential and differential models of system with acoustic feedback. The aim of the work is a for-mation, analysis and identification of linear and nonlinear functional differential models of echo, reverberation and acoustic feedback; the analysis of model sensitivity, the analysis of stability of telecommunication systems with the acoustic feedback. There is presented a mechanism of an acoustic feedback mechanism formation. 
 At the analysis of sound propagation in closed rooms with the use of the geometric acoustics method there is obtained a nucleus equation which is approximated by nonnegative functions taking into account a model of reverberation and a model of multiple reflections. The considered procedure of echo formation and reverberation is an element of the feedback model common for warning systems and technological communication. There is investigated a model of acoustic systems with delayed feedback. A diagram of the kernel of a functional differential equation describing a system with feedback is shown. 
 The models of systems with acoustic feedback presented in this work ensure the approximation to reality at that, an account of possibilities of the emergence in channels of non-linear distortion sound propagation are considered to be the next problem.

Particle filtering based parameter estimation for systems with output-error type model structures

The output-error model structure is often used in practice and its identification is important for analysis of output-error type systems. This paper considers the parameter identification of linear and nonlinear output-error models. A particle filter which approximates the posterior probability density function with a weighted set of discrete random sampling points is utilized to estimate the unmeasurable true process outputs. To improve the convergence rate of the proposed algorithm, the scalar innovations are grouped into an innovation vector, thus more past information can be utilized. The convergence analysis shows that the parameter estimates can converge to their true values. Finally, both linear and nonlinear results are verified by numerical simulation and engineering.

Recursive identification of block-oriented nonlinear systems in the presence of outliers

The paper considers the recursive identification of nonlinear (Hammerstein) model in the presence of outliers. In this model the nonlinear part is a polynomial of a known order in the input and linear part is described as an ARX (auto - regressive model with exogenous inputs) model. It is assumed that there is a priori information about a disturbance distribution in the form of a class of distributions. Owing that fact it is possible to use robust statistics in the sense of Huber. But Huber`s loss function is only first order differentiable. It follows that second order methods (Newton – Raphson methodology) cannot be used. The problem is avoided by analysis of the structure of least favourable distribution. It is shown that robust recursive algorithm derivation can be set in frame of l1−l2 – norm estimation problem. The main contributions of the paper are: (i) it is shown that the robust identification belongs to l1−l2 – norm estimation problem; (ii) the derivation of the new robust recursive algorithm; (iii) it is shown that robust recursive algorithm is switching algorithm (collection of linear least squares and sign algorithm) and that fact opens the new research opportunities.

A coupled approach for identification of nonlinear and compressible material models for soft tissue based on different experimental setups – Exemplified and detailed for lung parenchyma

In this paper, a coupled inverse analysis is proposed to identify nonlinear compressible hyperelastic material models described by two sets of experiments. While the overall approach is applicable for different materials, here it will be presented for viable lung parenchyma. Characterizing the material properties of lung parenchyma is essential to describe and predict the mechanical behavior of the respiratory system in health and disease. During breathing and mechanical ventilation, lung parenchyma is mainly subjected to volumetric deformations along with isochoric and asymmetric deformations that occur especially in diseased heterogeneous lungs. Notwithstanding, most studies examine lung tissue in predominantly isochoric tension tests. In this paper, we investigate the volumetric material behavior as well as the isochoric deformations in two sets of experiments: namely, volume–pressure-change experiments (performed with 287 samples of 26 rats) and uniaxial tension tests (performed with 30 samples of 5 rats). Based on these sets of experiments, we propose a coupled inverse analysis, which simultaneously incorporates both measurement sets to optimize the material parameters. Accordingly, we determine a suitable material model using the experimental results of both sets of experiments in one coupled identification process. The identified strain energy function with the corresponding material parameters Ψ=356.7Pa(I1−3)+331.7Pa(I3−1.075−1)+278.2Pa(I3−13I1−3)3+5.766Pa(I313−1)6 is validated to model both sets of experiments precisely. Hence, this constitutive model describes the complex volumetric and isochoric nonlinear material behavior of lung parenchyma. This derived material model can be used for nonlinear finite element simulations of lung parenchyma and will help to quantify the stresses and strains of lung tissue during spontaneous and artificial breathing; thus, allowing new insights into lung function and biology.

Two variants of the IIR spline adaptive filter for combating impulsive noise

It has been pointed out that the nonlinear spline adaptive filter (SAF) is appealing for modeling nonlinear systems with good performance and low computational burden. This paper proposes a normalized least M-estimate adaptive filtering algorithm based on infinite impulse respomse (IIR) spline adaptive filter (IIR-SAF-NLMM). By using a robust M-estimator as the cost function, the IIR-SAF-NLMM algorithm obtains robustness against non-Gaussian impulsive noise. In order to further improve the convergence rate, the set-membership framework is incorporated into the IIR-SAF-NLMM, leading to a new set-membership IIR-SAF-NLMM algorithm (IIR-SAF-SMNLMM). The proposed IIR-SAF-SMNLMM inherits the benefits of the set-membership framework and least-M estimate scheme and acquires the faster convergence rate and effective suppression of impulsive noise on the filter weight and control point adaptation. In addition, the computational burdens and convergence properties of the proposed algorithms are analyzed. Simulation results in the identification of the IIR-SAF nonlinear model show that the proposed algorithms offer the effectiveness in the absence of non-Gaussian impulsive noise and robustness in non-Gaussian impulsive noise environments.

Nonlinear Model Identification Methodology for Small, Fixed-Wing, Unmanned Aircraft

This paper describes system identification of a nonlinear flight dynamic model for a small, low-cost, fixed-wing unmanned aircraft with a limited instrumentation system. Unique challenges include greater sensitivity to atmospheric disturbances and degraded data quality. Methods are presented to improve the fidelity of the identified model, including use of the vortex lattice method to supplement flight-test data and the synthesis of data from distinct flight-test maneuvers. The parameter estimation strategy is based on the time-domain formulation of the output-error method using the nonlinear flight dynamic equations for a rigid aircraft with a nonlinear aerodynamic model. Methods are presented that increase the accuracy of parameter estimates compared with standard procedures based solely on flight-test data. The paper describes a detailed application of these procedures to a particular small, fixed-wing aircraft so that they can readily be adapted to other aircraft at a similar scale.

Robust identification approach for nonlinear state-space models

The identification of nonlinear state-space model (NSSM) with output observations corrupted by outliers is investigated in this paper. The outlier is commonly encountered in practical industrial processes which should not be ignored in nonlinear processes modeling. The statistical scheme based on the Student’s t-distribution is applied to resist the outlier and the expectation-maximization (EM) algorithm is employed to simultaneously identify the undetermined model and noise parameters. A particle smoother is introduced and used to approximately calculate the desired Q-function. The usefulness of the proposed approach is demonstrated via the numerical and mechanical examples.

System Identification of Nonlinear State-Space Models with Linearly Dependent Unknown Parameters Based on Variational Bayes

In this paper, we propose a parameter estimation method for nonlinear state-space models based on the variational Bayes. It is proved that the variational posterior distribution of the hidden state...

Non-destructive identification of maize haploid seeds using nonlinear analysis method based on their near-infrared spectra

The identification of maize haploid seeds is a significant process in genetic research and modern maize breeding. Adopting near-infrared spectroscopy technology to distinguish haploid seeds from hybrid seeds has the advantages of being non-destructive, rapid and low cost. However, due to the influence of light, temperature, humidity, near-infrared intensity, instrument and dynamic change of seed activity, the near-infrared spectra of maize seeds showed high dimensional nonlinear characteristics. In this study, to make full use of the class label information, a nonlinear feature analytical method for haploid maize seeds identification based on Supervised Virtual Sample Kernel Locality Preserving Projection (SVSKLPP) has been proposed. The experimental results showed that the nonlinear identification model SVSKLPP achieved strong classification performance to identify the maize haploid seeds. Moreover, compared with the linear feature extraction methods Principal Component Analysis, Orthogonal Linear Discriminant Analysis, Locality Preserving Projection, Supervised Virtual Sample Locality Preserving Projection and nonlinear feature extraction methods Kernel Locality Preserving Projection, Isomap, Locally Linear Embedding, Laplacian Eigenmaps and Local Tangent Space Alignment, the SVSKLPP model achieved a better performance. The average accuracy, sensitivity and specificity using method SVSKLPP were 97.1%, 98.8% and 95.4% respectively, and it also had high robustness. The overall results show that the SVSKLPP-NIR methodology was efficient in accurately identifying haploid maize seeds, thus demonstrating its capabilities for application in haploid breeding for crop variety improvement.

A nonlinear dynamic model and parameters identification method for predicting the shock pulse of rubber waveform generator

This paper proposed a highly accurate nonlinear dynamic model and parameters identification method to predict the shock pulses generated by rubber waveform generator (RWG) used in shock test. The establishment of the model is based on the primary results of the Duffing equation, Pan-Yang model and empirical stiffness formulae of cylindrical rubber isolator. We proposed a series of measures to eliminate the interferences in the drop shock test experiment, which are also of benefit to design, regulate and calibrate drop shock testers. The overall nonlinear system is solved in time domain with Runge–Kutta. And the parameters of the nonlinear dynamic model are identified by minimizing the holistic shape difference between experimental and predicted shock pulses with multiple population genetic algorithm. Meanwhile, the capacity of this model in characterizing the dynamic behavior of RWG under shock excitations is also investigated. Compared with previous work, our model considers nonlinear viscoelasticity of RWG, the geometric factor of RWG and the effect of initial shock velocity, which makes our model more accurate and general. Experimental results shown great agreements with the predictions and that the proposed method can determine the parameters conveniently and synergistically.

Identification of spin maneuver aerodynamic nonlinear model by applying ensemble empirical mode decomposition and extended multipoint modeling

Identification of the “aircraft aerodynamic model” in some unusual flight conditions such as spin maneuver provides critical information to the flight controller to retake the “dynamic stability” after it has been disturbed by the systematic, natural or environmental oscillations. Hence, a method for identifying the appropriate aerodynamic model in spin maneuvers is presented in this paper. We present an innovative systematic method for aerodynamic modeling of spin maneuvers, which combines the ensemble empirical mode decomposition technique and extended multipoint modeling approach, using flight data. In ensemble empirical mode decomposition, in addition to having all the empirical mode decomposition features, the original signal is collected with the white noise, and by using its statistical characteristics, the ensemble empirical mode decomposition solves the mode mixing problem. By applying the ensemble empirical mode decomposition to the flight parameter data, their intrinsic mode frequencies are extracted and are used as inputs to the extended multipoint modeling model. The extended multipoint modeling structure includes some parameters describing the distribution of aerodynamic forces and moments along each of the aircraft components. Moreover, this method allows coupling between the forces and moments. Unlike conventional methods, which consider the average forces obtained by plane surfaces relative to the center of mass, in the extended multipoint modeling technique, the force generated by each plane of the aircraft is allowed to appear independently in the motion equations. For identifying the aerodynamic model with extended multipoint modeling structure, the equation error method is used with a maximum likelihood optimizer inside. The obtained algorithm has been applied to two sets of spin maneuver flight data which were recorded in actual spin flight. The results demonstrate that the proposed method is able to reproduce the aerodynamic forces and moments for the second spin flight inputs with high accuracy by using a model which is derived from the first spin data identification.