Nonlinear System Identification Method Research Articles

A new method for hybrid-fuzzy identification

AbstractIn this paper a new identification method for non-linear hybrid systems that have mixed continuous and discrete states by using fuzzy clustering and principal component analysis is described. The method first determines the hybrid characteristic of the system inspired by an inverse form of the merge method for clusters, which makes it possible to identify the unknown switching points of a process based on just input-output data. Using the switching points, a hard partition of the input-output space is obtained. Then, we propose to use Takagi-Sugeno (TS) fuzzy models with Gaussian MFs as sub-models for each partition. Thus, the overall model is hybrid-fuzzy and will include explicitly the hybrid behavior of the system (the detected switching points) by means of binary MFs, and in each partition all the other non-linearities by means of TS sub-models. An illustrative experiment on a hybrid-tank system is conducted to present the benefits of the proposed approach.

Quasi-ARX wavelet network for SVR based nonlinear system identification

In this paper, quasi-ARX wavelet network (Q-ARX-WN) is proposed for nonlinear system identification. There are mainly two contributions are clarified. Firstly, compared with conventional wavelet networks (WNs), it is equipped with a linear structure, where WN is incorporated to interpret parameters of the linear ARX structure, thus Q-ARX-WN prediction model could be constructed and it is easy-to-use in nonlinear control. Secondly, guidelines for network construction are well considered due to the introduction of WNs, and Q-ARX-WN could be represented in a linear-in-parameter way. Therefore, linear support vector regression (SVR) based identification scheme may be introduced for the robust performance. Moreover, in adaptive control procedure, only linear parameters are needed to be adjusted when sudden changes have happened on the nonlinear system, thus the controller can track reference signal quickly. The effectiveness and robustness of the proposed nonlinear system identification method are validated by applying it to identify a real data system and a mathematical example, and an example of nonlinear system control is given to show usefulness of the proposed model.

Identification, prediction and detection of the process fault in a cement rotary kiln by locally linear neuro-fuzzy technique

In this paper, we use nonlinear system identification method to predict and detect process fault of a cement rotary kiln. After selecting proper inputs and output, an input–output model is identified for the plant. To identify the various operation points in the kiln, locally linear neuro-fuzzy (LLNF) model is used. This model is trained by LOLIMOT algorithm which is an incremental tree-structure algorithm. Then, using this method, we obtained 3 distinct models for the normal and faulty situations in the kiln. One of the models is for normal condition of the kiln with 15 min prediction horizon. The other two models are presented for the two faulty situations in the kiln with 7 min prediction horizon. At the end, we detect these faults in validation data. The data collected from White Saveh Cement Company is used in this study.

On climate reconstruction using bivalves: Three methods to interpret the chemical signature of a shell

To improve our understanding of the climate process and to assess the human impact on current global warming, past climate reconstruction is essential. The chemical composition of a bivalve shell is strongly coupled to environmental variations and therefore ancient shells are potential climate archives. The nonlinear nature of the relation between environmental condition (e.g. the seawater temperature) and proxy composition makes it hard to predict the former from the latter, however. In this paper we compare the ability of three nonlinear system identification methods to reconstruct the ambient temperature from the chemical composition of a shell. The comparison shows that nonlinear multi-proxy approaches are potentially useful tools for climate reconstructions and that manifold based methods result in smoother and more precise temperature reconstruction.

A global-local approach to nonlinear system identification: A review

We present the basic components of a time-domain nonlinear system identification (NSI) method with a promise of applicability to a broad class of smooth and non-smooth dynamical systems. The proposed NSI method is based on the close correspondence between analytical and empirical slow-flow dynamics, and relies on the direct analysis of measured time series without any a priori assumptions on the system dynamics; i.e. it is purely an output-based approach. The central assumption of the methodology is that the measured time series can be decomposed in terms of a finite number of oscillating components that are in the form of ‘fast’ monochromatic oscillations modulated by ‘slow’ amplitudes. The empirical slow-flow model of the dynamics is obtained from empirical mode decomposition (EMD), and its correspondence to the analytical slow-flow model establishes a local nonlinear interaction model (NIM). A NIM consists of a set of intrinsic modal oscillators (IMOs) that can reproduce the measured time series over different time scales and can account for (even strongly) nonlinear modal interactions. Hence, it represents a local model of the dynamics, identifying specific nonlinear transitions. An IMO, whose response can reproduce the corresponding intrinsic mode function acquired from EMD analysis, represents the dynamical characteristics of the system under certain initial or parameter conditions (i.e. local aspects). By collecting energy-dependent frequency behaviors from all identified IMOs, a frequency-energy plot (in the modal space) can be constructed, which depicts global features of the dynamical system. This represents a global model of the dynamics. We demonstrate the efficacy of the outlined global–local NSI method with two-degree-of-freedom dynamical systems—one smooth, and the other non-smooth. Copyright © 2010 John Wiley & Sons, Ltd.

A time-domain nonlinear system identification method based on multiscale dynamic partitions

Based on a theoretical foundation for empirical mode decomposition, which dictates the correspondence between the analytical and empirical slow-flow analyses, we develop a time-domain nonlinear system identification (NSI) technique. This NSI method is based on multiscale dynamic partitions and direct analysis of measured time series, and makes no presumptions regarding the type and strength of the system nonlinearity. Hence, the method is expected to be applicable to broad classes of applications involving time-variant/time-invariant, linear/nonlinear, and smooth/non-smooth dynamical systems. The method leads to nonparametric reduced order models of simple form; i.e., in the form of coupled or uncoupled oscillators with time-varying or time-invariant coefficients forced by nonhomogeneous terms representing nonlinear modal interactions. Key to our method is a slow/fast partition of transient dynamics which leads to the identification of the basic fast frequencies of the dynamics, and the subsequent development of slow-flow models governing the essential dynamics of the system. We provide examples of application of the NSI method by analyzing strongly nonlinear modal interactions in two dynamical systems with essentially nonlinear attachments.

Effective connectivity anomalies in human amblyopia

We investigate the effective connectivity in the lateral geniculate nucleus and visual cortex of humans with amblyopia. Six amblyopes participated in this study. Standard retinotopic mapping stimuli were used to define the boundaries of early visual cortical areas. We obtained fMRI time series from thalamic, striate and extrastriate cortical regions for the connectivity study. Thalamo-striate and striate-extrastriate networks were constructed based on known anatomical connections and the effective connectivities of these networks were assessed by means of a nonlinear system identification method. The effective connectivity of all networks studied was reduced when driven by the amblyopic eye, suggesting contrary to the current single-cell model of localized signal reduction, that a significant part of the amblyopic deficit is due to anomalous interactions between cells in disparate brain regions. The effective connectivity loss was unrelated to the fMRI loss but correlated with the degree of amblyopia (ipsilateral LGN to V1 connection), suggesting that it may be a more relevant measure. Feedforward and feedback connectivities were similarly affected. A hemispheric dependence was found for the thalamo-striate feedforward input that was not present for the feedback connection, suggesting that the reduced function of the LGN recently found in amblyopic humans may not be solely determined by the feedback influence from the cortex. Both ventral and dorsal connectivities were reduced.

Nonlinear System Identification Using Exponential Swept-Sine Signal

In this paper, we propose a method for nonlinear system (NLS) identification using a swept-sine input signal and based on nonlinear convolution. The method uses a nonlinear model, namely, the nonparametric generalized polynomial Hammerstein model made of power series associated with linear filters. Simulation results show that the method identifies the nonlinear model of the system under test and estimates the linear filters of the unknown NLS. The method has also been tested on a real-world system: an audio limiter. Once the nonlinear model of the limiter is identified, a test signal can be regenerated to compare the outputs of both the real-world system and its nonlinear model. The results show good agreement between both model-based and real-world system outputs.

ℒ2–ℒ∞ nonlinear system identification via recurrent neural networks

This paper proposes an ℒ2–ℒ∞ identification scheme as a new robust identification method for nonlinear systems via recurrent neural networks. Based on linear matrix inequality (LMI) formulation, for the first time, the ℒ2–ℒ∞ learning algorithm is presented to reduce the effect of disturbance to an ℒ2–ℒ∞ induced norm constraint. New stability results, such as boundedness, input-to-state stability (ISS), and convergence, are established in some senses. It is shown that the design of the ℒ2–ℒ∞ identification method can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. A numerical example is presented to demonstrate the validity of the proposed identification scheme.

Nonlinear Dynamic Modeling of Isometric Force Production in Primate Eye Muscle

Although the oculomotor plant is usually modeled as a linear system, recent studies of ocular motoneuron behavior have drawn attention to the presence of significant nonlinearities. One source of these is the development of muscle force in response to changes in motoneuron firing rate. Here, we attempt to simulate the production of isometric force by the primate lateral rectus muscle in response to electrical stimulation [A. Fuchs and E. Luschei, "Development of isometric tension in simian extraocular muscle," J. Physiol., vol. 219, no. 1, pp. 155-166, 1971] by comparing four different modeling approaches. The data could be well fitted either by parameter estimation for physically based models of force production [J. Bobet, E. R. Gossen, and R. B. Stein, "A comparison of models of force production during stimulated isometric ankle dorsiflexion in humans," IEEE Trans. Neural Syst. Rehabil. Eng., vol. 13, no. 4, pp. 444-451, Dec. 2005; E. Mavritsaki, N. Lepora, J. Porrill, C. H. Yeo, and P. Dean, "Response linearity determined by recruitment strategy in detailed model of nictitating membrane control," Biol. Cybern., vol. 96, no. 1, pp. 39-57, 2007], or by the application of a generic method for nonlinear system identification (the nonlinear autoregressive with exogenous input (NARX) model). These results suggest that nonlinear system identification may be a useful method for modeling more general aspects of muscle function, and provide a basis for distributed models of motor units in extraocular muscle for understanding dynamic oculomotor control. The success of previous linear models points to the potential importance of motor unit recruitment in overcoming nonlinearities in the oculomotor plant.

Non-linear system identification of gear crack failure based on second order Volterra kernel

Non-linear system identification has attracted great interest in mechanical fields. Against the weak vibration signals of gear crack failure and the considerable but ignored influence by input variation in gear tooth system non-linear working condition, which put forward a huge challenge to gear crack failure detection and identification's accurate, we have proposed a new non-linear non-parameter method that used the second order Volterra kernel function to analyse the inner contact between crack failure and the corresponding non-linear changes in whole system term. After identifying gear tooth system second order kernel function with input and output time series, we analysed the non-linear information indicated by frequency spectrum in detail. Anglicisation and comparison results show that gear tooth crack failure's second order Volterra kernel function considered the fault identification's correction influenced by input elements and was sensitive to system non-linear changes which were caused by different fault conditions. And, this non-linear system identification method can solve the diagnosis' fuzziness and indeterminacy problems caused by traditional frequency sideband theory. This new method is also helpful for mechanical system modelling, security running monitoring, dynamic design, the study of dynamic characteristics, and the fault diagnosis of rotary systems.

VERIFICATION OF IDENTIFICATION METHOD FOR NONLINEAR HYSTERETIC SYSTEMS UTILIZING SHAKING TABLE TESTS OF FULL-SCALE 4-STORY STEEL BUILDING

The already proposed identification method for nonlinear hysteretic systems is applied to shaking table tests of a full-scale 4-story steel building at the E-Defense. The structure is modeled as a 4DOF nonlinear shear building in each horizontal direction. The nonlinearity in stiffness is expressed as the Bouc-Wen hysteretic model. The identified hysteretic curve is compared to the corresponding experimental result.

Identification, Prediction and Detection of the Process Fault in a Cement Rotary Kiln by Locally Linear Neuro-Fuzzy Technique

Abstract In this paper, we use nonlinear system identification method to predict and detect process fault of a cement rotary kiln. After selecting proper inputs and output, an input–output model is identified for the plant. To identify the various operation points in the kiln, locally linear neuro-fuzzy (LLNF) model is used. This model is trained by LOLIMOT algorithm which is an incremental tree-structure algorithm. Then, using this method, we obtained 3 distinct models for the normal and faulty situations in the kiln. One of the models is for normal condition of the kiln with 15 min prediction horizon. The other two models are presented for the two faulty situations in the kiln with 7 min prediction horizon. At the end, we detect these faults in validation data. The data collected from White Saveh Cement Company is used in this study.

Advances in method of time-varying linear/nonlinear structural system identification and parameter estimate

The advances in methods of estimating modal parameters of a linear time-varying structural system and identifying dynamics characteristic of nonlinear time invariant structural systems in recent years are briefly reviewed. A parameter estimated procedure for linear time-varying structural system based on the subspace technology and nonlinear system identification method including scheme based on the neural networks and time varying NARMA (nonlinear auto regressive moving average) model is summarized in detail. Finally, major issues and directions for future work are discussed.

System Identification Using Optimally Designed Functional Link Networks via a Fast Orthogonal Search Technique

In this paper, a sparse nonlinear system identification method is proposed. Functional link neural nets (FLN) with their high orders polynomial basis functions are capable of performing complex nonlinear mapping. However, a large number of inputs and accurate modeling will require a huge number of basis functions that need to be explored. The Fast Orthogonal Search (FOS) introduced by Korenberg [1] is adopted here to detect the proper model and its associated parameters. The FOS algorithm is modified by first sorting all possible nonlinear functional expansion of the input pattern according to their correlation with the system output. The sorted functions are divided into equal size groups, pins, where functions with the highest correlation with the output are assigned to the first pin. Lower correlation members go the following pin and so forth. During the identification process, candidates in lower pins are tried first. If a solution is not found, next pins join the candidates pool for further modeling until the identification process completes within a prespecified accuracy. The proposed architecture is tested on noisefree and noisy nonlinear systems and shown to find sparse models that can approximate the experimented systems with acceptable accuracy.

Identification of Nonlinear Static Processes with Local Polynomial Regression and Subset Selection

The presented method for nonlinear system identification is based on the LOLIMOT algorithm introduced by Nelles and Isermann [1996]. The LOLIMOT algorithm divides the input space by a tree-construction algorithm and interpolates the local linear models by local membership functions. Instead of assuming local linear models, the presented algorithm utilizes general local nonlinear functions, which make the algorithm more flexible. These are approximated by a multidimensional Taylor series. Since the amount of regressors grows fast with the number of inputs and the expansion order, a subset selection procedure is introduced. It reveals significant regressors and gives information about the local functional behavior. The local subset selection is implemented as a stepwise regression with replacement of regressors. Mallows’ Cp-statistic is used for the subset selection algorithm and is also implemented for final model selection. The benefit of the extended algorithm lies in the higher flexibility in the local models, which results in less partitions of the input space by a similar approximation quality.

On Climate Reconstruction using Bivalve Shells: Three Methods to Interpret the Chemical Signature of a Shell

The chemical composition of a bivalve shell is strongly coupled to the seasonal variations in the environment. The nonlinear nature of this relation however makes it hard to predict, e.g. the temperature, from the chemical composition of a shell. In this paper we compare the ability of three nonlinear system identification methods to reconstruct the temperature from the chemical composition of a shell. The comparison shows that nonlinear multi-proxy approaches are potential tools for climate reconstructions with a preference for manifold based methods that results in smoother and a more precise temperature reconstruction.

The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing

The use of heterogeneous, non-collocated measurements for nonlinear structural system identification is explored herein. In particular, this paper considers the example of sensor heterogeneity arising from the fact that both acceleration and displacement are measured at various locations of the structural system. The availability of non-collocated data might often arise in the identification of systems where the displacement data may be provided through global positioning systems (GPS). The well-known extended Kalman filter (EKF) is often used to deal with nonlinear system identification. However, as suggested in (J. Eng. Mech. 1999; 125(2):133–142), the EKF is not effective in the case of highly nonlinear problems. Instead, two techniques are examined herein, the unscented Kalman filter method (UKF), proposed by Julier and Uhlman, and the particle filter method, also known as sequential Monte Carlo method (SMC). The two methods are compared and their efficiency is evaluated through the example of a three degree-of-freedom system, involving a Bouc–Wen hysteretic component, where the availability of displacement and acceleration measurements for different DOFs is assumed. Copyright © 2008 John Wiley & Sons, Ltd.

Nonlinear system identification of automotive dampers: A time and frequency-domain analysis

This paper provides an overview of a number of nonlinear system identification methods as applied to the analysis of nonlinear automotive dampers. The motivation for illustrating a number of approaches is that each method provides different insights into the behavior of the systems and therefore the methods are complementary. The background for each of the methods is given and each is demonstrated through an experimental case study.

Nonlinear Model-Based System Identification of Lead–Rubber Bearings

A nonlinear model-based system identification method is proposed, formulated, implemented, and applied to a three-span continuous base-isolated bridge. Transverse and rotational rigid-body motions of the bridge superstructure are formulated into two degrees-of-freedom dynamic governing equations. To model hysteretic behavior of lead–rubber bearings, the Menegotto–Pinto model is used. The proposed system identification procedures consist of two phases to address ill-conditioning issues. The uncertainty of parameters is considered, which results in probability distributions instead of single values for identified parameters. The proposed system identification is adopted in the comparison of experimental data sets. Hypothesis testing is used to determine the closeness of identification results. The proposed method is applied to quick-release field experiments on the bridge to investigate aging and temperature dependent effects in lead–rubber bearings.