Nonlinear System Identification Procedure Research Articles

Nonlinear-Control-Oriented Modeling of the Multi-Variable Underground Coal Gasification Process for UCG Project Thar: A Machine Learning Perspective

The Underground Coal Gasification (UCG) process is a complex and multi-physics phenomenon, thus making it difficult to develop a mathematical model that encapsulates all dynamical aspects. In this regard, data-driven modeling techniques offer a reliable alternative for prediction, control, and optimization of dynamical systems, but their application in UCG is still in the early stages. This work aims to bridge this gap by implementing three cutting-edge nonlinear identification structures: Non-linear Autoregressive with Exogenous Inputs (NARX), Hammerstein–Wiener (HW), and State-Space Neural Networks (SSNN) on the UCG process to obtain a multivariable control-oriented model. The contributions include synthesizing an excitation signal for data acquisition, outlining the non-linear system identification procedure, and comparing predictive capabilities using statistical tools. The simulation results demonstrate a rigorous comparison of various techniques for the heating value and flowrate of the syngas, which are the outputs of the UCG process. The results of the analysis show that NARX outperforms other structures in statistical metrics, with MAE, RMSE, and Best fit values of 1.51,1.9, and 0.9, respectively, for the heating value; and 0.25,0.31, and 0.94, respectively, for the flowrate. Consequently, the outputs of the NARX model are compared with the experimental data obtained from the UCG project Thar, which show a good match for both outputs.

Nonlinear parameter estimation in damping with volterra series through harmonic probing

In this work nonlinear system identification procedure, based on Volterra series, is presented to distinguish a damping nonlinearity from stiffness nonlinearity, using measured first and third harmonic amplitude characteristics. First and higher order volterra kernel synthesis formulations and frequency response functions (FRFs) have been developed in damping and stiffness nonlinearity. The characteristics of first and higher order harmonic amplitudes at various excitation level is studied for the both the nonlinearity. This paper shows comparison study between the Volterra series, Runge-Kutta fourth order in analysis of damping and stiffness nonlinearity in the mechanical systems. Nonlinearity can lead to various system behaviour, like jump phenomenon, stable and unstable region, super harmonic resonances. Using first and higher order harmonic amplitudes, formulated from Volterra series response representation, nonlinear parameters are estimated through the recursive iteration method.

Characteristic nonlinear system identification: A data-driven approach for local nonlinear attachments

Abstract This research introduces the characteristic nonlinear system identification (CNSI) procedure for identifying the dynamics of local nonlinear attachments. Unlike many existing methods, the CNSI method requires no prior knowledge or models of the dynamics governing the parent structure or the attachment. Instead, the CNSI technique relies entirely on post-processing of the measured transient response of the attachment and its connection points to the base structure (such that the relative motion can be computed), its mass and a proposed model for its dynamics. The CNSI approach is divided into two phases: a data-processing phase and a model-identification phase. In the first phase, the measured response is post-processed to obtain characteristic displacements and velocities, and instantaneous frequency and damping curves. In the second phase, the analyst proposes a model for the dynamics of the attachment and performs a systematic identification for the unknown parameters using the post-processed data. The result is a reduced-order model, including both nonlinear stiffness and damping, that captures the physics governing the response of the attachment. The CNSI method is demonstrated experimentally using the response of a linear oscillator with a smooth nonlinear attachment.

Time-series-based nonlinear system identification of strongly nonlinear attachments

This work introduces a new nonlinear system identification procedure for identifying the dynamics of an otherwise linear mechanical system augmented by strongly nonlinear local attachments directly from measured transient response data. The method employs the proper orthogonal decomposition to extract energy-dependent proper orthogonal modes from the measured time series. Then, using known linear properties, the characteristic frequencies of the system are estimated by applying the Rayleigh quotient, and an estimated frequency-energy plot (FEP) is created by plotting the characteristic frequencies as functions of the mechanical energy in the system. The estimated FEP directly reveals the presence of strongly nonlinear modal interactions, in the form of non-smooth perturbations (spikes) that result from transient resonance captures between different harmonic components of the measured data. The nonlinearity is identified by plotting the estimated characteristic frequencies as functions of a defined characteristic displacement and fitting a frequency equation based on the model of the nonlinearity. The method is demonstrated computationally and experimentally using the response of a cantilevered model airplane wing with a strongly nonlinear attachment connected to its tip.

Nonlinear system identification from noisy measurements

A novel nonlinear system identification procedure using noisy measurements for health assessment of real civil infrastructure systems is presented. The important features of the procedure are that it can identify a structural system using only a limited number of highly noise-contaminated responses measured for a very short duration. To compensate for the use of very short duration response time-histories, multiple weighted global iteration (WGI) procedure is introduced in the unscented Kalman filter (UKF) algorithm to help the convergence process. It is denoted as UKF-WGI procedure. The algorithm is a finite element-based nonlinear system identification technique. It identifies not only the integrity of the whole structure, but also the locations and severity of the defects. Since no similar studies are reported in the literature, the superiority of UKF-WGI over the extended Kalman filter-based procedure in the presence of noise is established with the help of several illustrative examples.

A PSO-Based Fuzzy c-Regression Model Applied to Nonlinear Data Modeling

This paper presents a new method for fuzzy c-regression models clustering algorithm. The main motivation for this work is to develop an identification procedure for nonlinear systems using weighted recursive least squares and particle swarm optimization. The fuzzy c-regression models algorithm is sensitive to initialization which leads to the convergence to a local minimum of the objective function. In order to overcome this problem, particle swarm optimization is employed to achieve global optimization of FCRM and to finally tune parameters of obtained fuzzy model. The weighted recursive least squares is used to identify the unknown parameters of the local linear model. Finally, validation results involving simulation of two examples have demonstrated the effectiveness and practicality of the proposed algorithm.

Recurrent-neural-network-based identification of a cascade hydraulic actuator for closed-loop automotive power transmission control

By virtue of its ease of operation compared with its conventional manual counterpart, automatic transmissions are commonly used as automotive power transmission control system in today’s passenger cars. In accordance with this trend, research efforts on closed-loop automatic transmission controls have been extensively carried out to improve ride quality and fuel economy. State-of-the-art power transmission control algorithms may have limitations in performance because they rely on the steady-state characteristics of the hydraulic actuator rather than fully exploit its dynamic characteristics. Since the ultimate viability of closed-loop power transmission control is dominated by precise pressure control at the level of hydraulic actuator, closed-loop control can potentially attain superior efficacy in case the hydraulic actuator can be easily incorporated into model-based observer/controller design. In this paper, we propose to use a recurrent neural network (RNN) to establish a nonlinear empirical model of a cascade hydraulic actuator in a passenger car automatic transmission, which has potential to be easily incorporated in designing observers and controllers. Experimental analysis is performed to grasp key system characteristics, based on which a nonlinear system identification procedure is carried out. Extensive experimental validation of the established model suggests that it has superb one-step-ahead prediction capability over appropriate frequency range, making it an attractive approach for model-based observer/controller design applications in automotive systems.

Nonlinear model identification of an experimental ball-and-tube system using a genetic programming approach

Most processes in industry are characterized by nonlinear and time-varying behavior. The identification of mathematical models typically nonlinear systems is vital in many fields of engineering. The developed mathematical models can be used to study the behavior of the underlying system as well as for supervision, fault detection, prediction, estimation of unmeasurable variables, optimization and model-based control purposes. A variety of system identification techniques are applied to the modeling of process dynamics. Recently, the identification of nonlinear systems by genetic programming (GP) approaches has been successfully applied in many applications. GP is a paradigm of evolutionary computation field based on a structure description method that applies the principles of natural evolution to optimization problems and its nature is a generalized hierarchy computer program description. GP adopts a tree structure code to describe an identification problem. Unlike the traditional approximation methods where the structure of an approximate model is fixed, the structure of the GP tree itself is modified and optimized and, thus, there is a possibility that GP trees could be more appropriate or accurate approximate models. This paper focuses the GP method for structure selection in a system identification applications. The proposed GP method combines different techniques for tuning of crossover and mutation probabilities with an orthogonal least-squares (OLS) algorithm to estimate the contribution of the branches of the tree to the accuracy of the discrete polynomial Nonlinear AutoRegressive with eXogenous inputs (NARX) model. The nonlinear system identification procedure, based on a NARX representation and GP, is applied to empirical case study of an experimental ball-and-tube system. The results demonstrate that the GP with OLS is a promising technique for NARX modeling.

Identification of Nonlinear Feedback Systems Using a Structured Polynomial Nonlinear State Space Model

In this paper, we propose an identification procedure for nonlinear feedback systems by introducing a new type of model structure. The idea is to combine the advantages of two different model structures: the Polynomial NonLinear State Space (PNLSS) model and the block-structured feedback model. By imposing structural information to the existing PNLSS model, we obtain a flexible model with a lower number of parameters compared with the unconstrained structure. The structured-PNLSS model consists of a linear block in the feedforward path and a PNLSS block in the feedback path. The presented identification procedure for the structured-PNLSS model is applied to input/output measurements of a nonlinear device.

Wavelet Neural Network Based Indirect Adaptive Control of Chaotic Nonlinear Systems

In this paper, we present a indirect adaptive control method using a wavelet neural network (WNN) for the control of chaotic nonlinear systems without precise mathematical models. The proposed indirect adaptive control method includes the off-line identification and on-line control procedure for chaotic nonlinear systems. In the off-line identification procedure, the WNN based identification model identifies the chaotic nonlinear system by using the serial-parallel identification structure and is trained by the gradient-descent method. And, in the on-line control procedure, a WNN controller is designed by using the off-line identification model and is trained by the error back-propagation algorithm. Finally, the effectiveness and feasibility of the proposed control method is demonstrated with applications to the chaotic nonlinear systems.

Characterizing cochlear mechano-electric transduction with a nonlinear system identification technique: the influence of the middle ear.

Previously a third-order polynomial equation characterizing mechano-electric transduction was obtained from a nonlinear system identification procedure applied to an ear canal acoustic signal and cochlear microphonic (CM/AC). In this paper, we examine the influence of the linearity and frequency response of the intervening middle ear on the nonlinearity, frequency response, and coherence of the third-order polynomial model of mechano-electric transduction (MET). Ear canal sound pressure (AC), cochlear microphonics (CM), and stapes velocity (SV) were simultaneously recorded from Mongolian gerbils. Linear and nonlinear transfer and coherence functions relating stapes velocity to the acoustic signal (SV/AC), CM to the acoustic signal (CM/AC), and CM to the stapes velocity (CM/SV) were computed. The results showed that SV/AC was linear while CM/AC and CM/SV were not, indicating that the nonlinearity of CM/AC was not due to nonlinearity of the middle ear. The frequency response of the linear term of CM/AC was similar to that of ST/AC but differed from that of CM/SV while the cubic term of CM/AC was similar to that of CM/SV. This indicates that the frequency dependence of CM/AC was due to both the middle ear and frequency dependence of the inner ear. Finally the fit of the polynomial model of MET without the middle ear (CM/SV) did not improve from the fit including the middle ear (CM/AC). A cochlear model of the CM indicated that the lack of improvement was due to the limitations of a third-order polynomial equation characterizing the hair cell transducer function.

POLYNOMIAL ARTIFICIAL NEURAL NETWORK AND GENETIC ALGORITHM FOR THE IDENTIFICATION AND CONTROL OF NONLINEAR SYSTEMS

In Adaptive Control Theory there are different procedures to identify a linear system. The fundamental problem is that in the real world many systems are nonlinear and it is not easy to obtain a mathematical model. In this work, an identification procedure for nonlinear systems is presented using the properties of Artificial Neural Networks and Genetic Algorithms to optimize the architecture of the network. A new technique of Adaptive Control to cancel the nonlinear dynamics of the system is proposed to set the poles of the system in a desire position. The behavior of the algorithm for the linear and nonlinear case is presented with the analysis of the theory and operational importance of these techniques.

A novel nonlinear system identification technique for modeling cochlear transduction using otoacoustic emissions data

A novel mathematical technique is presented for modeling the linear and nonlinear properties of the cochlear transduction process. This new nonlinear system identification procedure (Bendat, 1990) has several advantages over classical techniques used for analyzing nonlinear systems. With this technique, nonlinear systems may be modeled as a linear system in parallel with any number of finite-memory nonlinear systems. Higher-order nonlinear terms can be more easily computed with this technique than with others such as volterra kernel analysis. Furthermore, a broadband signal such as a transient signal can be used to characterize the cochlea over a wide frequency band. This makes the application of this procedure ideal for modeling cochlear transduction process with transient evoked otoacoustic emissions data. Otoacoustic emissions were recorded in response to finite impulse response (FIR) pulses from 11 subjects with normal hearing. System identification procedures were implemented using third- and fifth-order polynomial models. Based on the input and output records, system properties were estimated. Coherence measures tested the goodness-of-fit of the chosen model. The identified systems were used to predict the systems’ response to two-tone stimuli. The fifth-order model predictions were in better accordance with previously reported data on acoustic distortion products.

Orthogonalised frequency domain volterra model for non-gaussian inputs

An orthogonalised Volterra system model, valid for both non-Gaussian and Gaussian inputs, is presented. The approach is based on ordered sets of conditioned orthogonal higherorder input vectors in the frequency domain, and utilises co-ordinate transformation to relate the orthogonal and nonorthogonal system models. The orthogonal model exhibits no interference effects, thus facilitating physical interpretation of the nonlinear system model. The importance of non-Gaussian excitation in the nonlinear system identification procedure is discussed. The performance of the orthogonalised Volterra model is measured in terms of a generalised nonlinear system coherence function, and compared with the results of the Wiener (for Gaussian input) and Volterra models. The advantages of the orthogonalised Volterra model are illustrated by using it to model the linear and quadratic responses of a tension leg platform subject to random seas, given experimental input-output time series data.