Nonlinear System Identification Model Research Articles

On the dynamic properties of statistically-independent nonlinear normal modes

Much attention has been given to the study of nonlinear normal modes (NNMs), a nonlinear extension to the eminently useful framework for the analysis of linear dynamics provided by linear modal analysis (LMA). In the literature, several approaches have gained traction, with each able to preserve a subset of the useful properties of LMA. A recently-proposed framework (Worden and Green, 2017) casts nonlinear modal analysis as a problem in machine learning, viewing the NNM as directions in a latent modal coordinate space within which the modal dynamics are statistically uncorrelated. Thus far, the performance of this framework has been measured in a largely qualitative way. This paper presents, for the first time, an exploration into the underlying dynamics of the statistically-independent NNMs using techniques from nonlinear system identification (NLSI) and higher-order frequency-response functions (HFRFs).In this work, the statistically-uncorrelated NNMs are found for two simulated nonlinear cubic-stiffness systems using a recently-proposed neural-network based approach. NLSI models are fitted to both physical and modal displacements and the HFRFs of these models are compared to theoretical values. In particular, it is found for both systems that the modal decompositions here permit an independent single-input single-output (SISO) representation that can be projected back onto the original displacements with low error. It is also shown via the HFRFs that the underlying linear natural frequencies of the modal dynamics lie very close to the underlying linear natural frequencies of the nonlinear systems, indicating that a true nonlinear decomposition has been identified.

An Operando calorimeter for high temperature electrochemical cells

Operando calorimetry has previously been utilized to study electrochemical reactions and degradation in electrochemical cells such as batteries. Calorimetric data can provide important information on the lifetime and thermal properties of electrochemical cells in practical engineering applications such as thermal management. High temperature electrochemical cells such as solid oxide fuel cells or electrolyzers can also benefit from operando calorimetry, but to the authors’ knowledge such capabilities have not been commercially developed. Herein, an operando calorimeter is reported that is capable of simultaneous calorimetry and electrochemistry at temperatures up to 1000 °C and in both oxidizing and reducing atmospheres. The calorimeter is constructed by modifying a commercial apparatus originally designed to study high temperature electrochemical cells in various gas environments. A grey-box, nonlinear system identification model is utilized to analyze both electrochemical and calorimetric data of BaZr0.8Ce0.1Y0.1O3 based electrochemical cells and achieve a calorimeter electrochemical cell power sensitivity of 16.1 ± 11.7 mW. This operando calorimeter provides the capability to study thermal behaviour of electrochemical cells at elevated temperatures.

Nonlinear Data-Based Hydrodynamic Modeling of a Fixed Oscillating Water Column Wave Energy Device

System identification (SI) techniques represent an alternative strategy to provide the hydrodynamic model of oscillating water column (OWC) devices, compared to more traditional physics-based methods, such as linear potential theory (LPT) and computational fluid dynamics (CFD). With SI, the parameters of the model are obtained, by minimizing a model-related cost function, from input-output data. The main advantage of SI is its simplicity, as well as its potential validity range, where the dynamic model is valid over the full range for which the identification data was recorded. The paper clearly shows the value of a global nonlinear model, both in terms of accuracy and computational simplicity, over an equivalent multi-linear modelling solution. To this end, the validation performance of the nonlinear model is compared to the results provided by a range of linear models. Furthermore, in order to provide a more comprehensive comparative analysis, some practical aspects related to real-time implementation of multi-linear and nonlinear SI models are discussed. For the experimental campaign, real wave tank (RWT) data of a scaled OWC model are gathered from the narrow tank experimental facility at Dundalk Institute of Technology (DkIT). Particular attention is paid to the selection of suitable input signals for the experimental campaign, in order to ensure that the model is subjected to the entire range of equivalent frequencies, and amplitudes, over which model validity is required.

Nonlinear system identification model of the spread of TB disease using the genetic algorithm and multilayer perceptron

System identification is the process of building a mathematical model of a dynamic system based on the observed input-output data. Artificial neural networks have been shown to complete the identification of nonlinear systems with various learning algorithms. Identification of nonlinear dynamic systems in the model of TB disease spread is needed to predict the spread of TB disease. The model for the spread of TB disease has three compartments and six parameters. The process of identifying models for the spread of TB disease by estimating parameters using the genetic algorithm and validation of the model using multilayer perceptron. The choice of multilayer perceptron architecture determines the minimum error in the nonlinear system identification process for the model of TB disease spread. From the results of the trial, it was shown that the multilayer perceptron and genetic algorithm were able to identify the spread model of TB disease with MMRE of 0.00347

Estimating groundwater levels using system identification models in Nzhelele and Luvuvhu areas, Limpopo Province, South Africa

This study was focused on testing the ability of a coupled linear and non-linear system identification model in estimating groundwater levels. System identification provides an alternative approach for estimating groundwater levels in areas that lack data required by physically-based models. It also overcomes the limitations of physically-based models due to approximations, assumptions and simplifications. Daily groundwater levels for 4 boreholes, rainfall and evaporation data covering the period 2005–2014 were used in the study. Seventy and thirty percent of the data were used to calibrate and validate the model, respectively. Correlation coefficient (R), coefficient of determination (R2), root mean square error (RMSE), percent bias (PBIAS), Nash Sutcliffe coefficient of efficiency (NSE) and graphical fits were used to evaluate the model performance. Values for R, R2, RMSE, PBIAS and NSE ranged from 0.8 to 0.99, 0.63 to 0.99, 0.01–2.06 m, −7.18 to 1.16 and 0.68 to 0.99, respectively. Comparisons of observed and simulated groundwater levels for calibration and validation runs showed close agreements. The model performance mostly varied from satisfactory, good, very good and excellent. Thus, the model is able to estimate groundwater levels. The calibrated models can reasonably capture description between input and output variables and can, thus be used to estimate long term groundwater levels.

Identification of the Response of a Controlled Building Structure Subjected to Seismic Load by Using Nonlinear System Models

The present study investigates the prediction efficiency of nonlinear system-identification models, in assessing the behavior of a coupled structure-passive vibration controller. Two system-identification models, including Nonlinear AutoRegresive with eXogenous inputs (NARX) and adaptive neuro-fuzzy inference system (ANFIS), are used to model the behavior of an experimentally scaled three-story building incorporated with a tuned mass damper (TMD) subjected to seismic loads. The experimental study is performed to generate the input and output data sets for training and testing the designed models. The parameters of root-mean-squared error, mean absolute error and determination coefficient statistics are used to compare the performance of the aforementioned models. A TMD controller system works efficiently to mitigate the structural vibration. The results revealed that the NARX and ANFIS models could be used to identify the response of a controlled structure. The parameters of both two time-delays of the structure response and the seismic load were proven to be effective tools in identifying the performance of the models. A comparison based on the parametric evaluation of the two methods showed that the NARX model outperforms the ANFIS model in identifying structures response.

D-RM Builder: A software tool for generating fast and accurate nonlinear dynamic reduced models from high-fidelity models

Abstract Dynamic reduced models (D-RMs) derived from rigorous models are highly desired for speeding up dynamic simulations. A useful software tool named D-RM Builder was developed to automatically generate data-driven D-RMs from high-fidelity dynamic models. It allows a user to configure input/output variables, sample input space and generate sequences of step changes, launch high-fidelity model simulations, fit simulation results to a D-RM, and finally visualize and validate the D-RM. The Decoupled A-B Net (DABNet) nonlinear system identification model was used as the main D-RM type and was enhanced to model nonlinear multiple input and multiple output dynamic systems with options for double-pole formulation to handle fast/slow time scales and pole value optimization. The D-RM Builder tool has been successfully used to generate D-RMs for a highly nonlinear pH neutralization reactor system and a two-time-scale bubbling fluidized bed adsorber-reactor for CO2 capture.

Fuzzy functions with function expansion model for nonlinear system identification

AbstractIn this study, the structure of fuzzy functions is improved by function expansion. Unlike fuzzy conventional if-then rules, classical fuzzy function structure includes fuzzy bases and linear inputs. Membership functions of fuzzy bases are set using fuzzy C-means (FCM) algorithm, and the linear parameters are computed using the least-square estimation (LSE). This study has two main contributions. First, conventional “fuzzy functions” structure is powered by the expansion of orthogonal “trigonometric functions” where the approximation capabilities of the fuzzy functions are increased. Second, the widths of the normalized membership functions determined for the fuzzy function model are optimized using the Nelder-Mead simplex algorithm that provides further enhancement on the identification performance. The advantages of the proposed model are shown via offline identification of a benchmark nonlinear system and online identification of two real-time nonlinear systems.

A Developed Local Polynomial Neuro-Fuzzy Model for Nonlinear System Identification

This paper proposes a local polynomial model tree (LPMT) learning technique for prediction and identification of nonlinear systems and processes. The proposed LPMT learning algorithm is applied to a local polynomial neuro fuzzy (LPNF) model, which includes local polynomial models (LPMs), as Taylor series expansion of any unknown function. . The LPMT algorithm is established based on the concept of hierarchical binary tree and heuristically partitions the input space into smaller subdomains through axis-orthogonal splits. The proposed learning algorithm starts from a single local polynomial model and then refines the LPNF model by increasing the degree of the worstperforming LPM or by further partitioning of the input space. During the learning procedure, the validity functions automatically form a partition of unity and therefore normalization side effects, e.g. reactivation and poor extrapolation performance, are prevented. The LPNF model, trained by the proposed LPMT algorithm, is used for prediction and identification of the nonlinear processes and systems in three case studies. The obtained results and comparisons to other methods revealed the promising performance of the proposed model.

Multivariable nonlinear identification of smart buildings

This paper presents a new multi-input–multi-output (MIMO) fuzzy model for nonlinear system identification (SI) of smart structures under a variety of random forces. The fuzzy SI model is developed through the integration of wavelet transform (WT), multiple MIMO linear autoregressive exogenous (ARX) input models, Takagi–Sugeno (TS) fuzzy model, weighted linear least squares, and data clustering algorithms: MIMO WARX-TS fuzzy model. To demonstrate the effectiveness of the MIMO WARX-TS fuzzy model, a three-story building equipped with a magnetorheological (MR) damper under a variety of random signals is investigated. To train the proposed model, an artificial earthquake and control forces are used as input signals while displacement and acceleration responses are used as outputs. To validate the trained model, four real recorded earthquake signals are used. It is shown from the simulation that the proposed MIMO WARX-TS fuzzy identification algorithm is effective in estimating nonlinear behavior of a building–MR damper system under a variety of seismic excitations.

Heat transfer analysis of unsteady graphene oxide nanofluid flow using a fuzzy identifier evolved by genetically encoded mutable smart bee algorithm

In the current research, the unsteady two dimensional Graphene Oxide water based nanofluid heat transfer between two moving parallel plates is analyzed using an intelligent black-box identifier. The developed intelligent tool is known as evolvable evolutionary fuzzy inference system (EE-FIS) which is based on the integration of low-level fuzzy programming and hyper-level evolutionary computing concepts. Here, the authors propose the use of a modified evolutionary algorithm (EA) which is called hybrid genetic mutable smart bee algorithm (HGMSBA). The proposed HGMSBA is used to evolve both antecedent and consequent parts of fuzzy rule base. Besides, it tries to prune the rule base of fuzzy inference system (FIS) to decrease its computational complexity and increase its interpretability. By considering the prediction error of the fuzzy identifier as the objective function of HGMSBA, an automatic soft interpolation machine is developed which can intuitively increase the robustness and accuracy of the final model. Here, HGMSBA-FIS is used to provide a nonlinear map between inputs, i.e. nanoparticles solid volume fraction (ϕ), Eckert number (Ec) and a moving parameter which describes the movements of plates (S), and output, i.e. Nusselt number (Nu). Prior to proceeding with the modeling process, a comprehensive numerical comparative study is performed to investigate the potentials of the proposed model for nonlinear system identification. After demonstrating the efficacy of HGMSBA for training the FIS, the system is applied to the considered problem. Based on the obtained results, it can be inferred that the developed HGMSBA-FIS black-box identifier can be used as a very authentic tool with respect to accuracy and robustness. Besides, as the proposed black-box is not a physics-based identifier, it frees experts from the cumbersome mathematical formulations, and can be used for advanced real-time applications such as model-based control. The simulations indicate that the gradient of Nu has a direct nonlinear relation with the values of ϕ and Ec. It is also observed that an increase in the value of S decreases the value of Nu.

Nonlinear System Identification via Basis Functions Based Time Domain Volterra Model

This paper proposes basis functions based time domain Volterra model for nonlinear system identification. The Volterra kernels are expanded by using complex exponential basis functions and estimated via genetic algorithm (GA). The accuracy and practicability of the proposed method are then assessed experimentally from a scaled 1:100 model of a prototype truss spar platform. Identification results in time and frequency domain are presented and coherent functions are performed to check the quality of the identification results. It is shown that results between experimental data and proposed method are in good agreement.

Neural network design and model reduction approach for black box nonlinear system identification with reduced number of parameters

In this paper a dedicated recurrent neural network design and a model reduction approach are proposed in order to improve the balance between complexity and quality of black box nonlinear system identification models. The proposed neural network design, based on a three-layers architecture, helps to reduce the number of parameters of the model after the training phase without any significant loss of estimation accuracy. Nevertheless, the proposed architecture remains sufficiently general to provide a wide range of models among the most encountered in the literature. This reduction, achieved by a convenient choice of the activation functions and the initial conditions of the synaptic weights, is developed in two steps. The first step is to train the proposed architecture under two reasonable assumptions. Then the recurrent three-layers neural network is transformed into a representation of two-layer with less number of neurons, that is, a significant reduced number of parameters. The constructed architecture provided models with reasonable reduced number of parameters with a convenient estimation accuracy. To validate the proposed approach, we identify the Wiener–Hammerstein benchmark nonlinear system proposed in SYSID2009 [1].

Identification of a parametric loudspeaker system using an adaptive Volterra filter

Due to the parametric acoustic array effect in air, the input audible signal of a parametric loudspeaker system can be reproduced with high directivity at the target region. However, the reproduced audible signal suffers from harmonic distortion, which is the by-product of nonlinear interaction between the primary waves. In order to investigate this inherent nonlinear phenomenon, a nonlinear system identification model is developed based on an adaptive Volterra filter. Unlike the conventional loudspeaker, the nonlinear characteristic of a parametric loudspeaker system is dependent on several primary parameters in nonlinear acoustics, which include the initial pressure of the primary waves, the observing distance and angle, as well as ambient temperature and relative humidity. By using a truncated Volterra series up to the 2nd-order kernel, numerical simulations are conducted to develop a system model with one group of parameters and examine the quadratic nonlinear intensity for different parameters’ settings. Experimental measurements, which take into account of emitter’s response, are carried out to verify the modeling result and evaluate the model performance. Based on the Volterra system model, the sound pressure level and the harmonic distortion can be accurately predicted.

A New Hammerstein Model for Non-Linear System Identification

In the present work a newer type of black box nonlinear model in Hammerstein structure is proposed. The model has Wavelet Network coupled with Orthonormal Basis Functions which is capable of modeling a class of non-linear systems with acceptable accuracy. Wavelet basis functions have the property of localization in both the time and frequency domains which enables wavelet networks to approximate severe non-linearities using few number of parameters. Orthonormal Basis functions possess the ability to approximate any linear time invariant system using appropriate basis functions. The efficacy of the model in modeling is demonstrated using numerical examples.

MIMO fuzzy identification of building-MR damper systems

This paper proposes a multi-input, multi-output (MIMO) nonlinear system identification (SI) of civil structures equipped with magnetorheological (MR) dampers. The nonlinear SI model is developed through the integration of multiple MIMO autoregressive exogenous (ARX) input models, Takagi-Sugeno (TS) fuzzy model, weighted linear least squares, fuzzy C-means and subtractive clustering algorithms. To demonstrate the effectiveness of the MIMO ARX-TS fuzzy model, a seismically excited three-story building equipped with an MR damper is investigated: Parameters of the premise and consequent parts for the proposed model are represented in detail and comparison between the original data and identified one is given. It is shown from the simulation that the proposed nonlinear MIMO ARX-TS fuzzy identification algorithm is effective in estimating nonlinear behavior of a seismically excited building-MR damper system.

Statistical analysis of the single-layer backpropagation algorithm: Part I - Mean weight behavior

The single-layer backpropagation algorithm is a gradient-descent method that adjusts the connection weights of a single-layer perceptron to minimize the mean-square error at the output. It is similar to the standard least mean square al- gorithm, except the output of the linear combiner contains a differentiable nonlinearity. In this paper, we present a statis- tical analysis of the mean weight behavior of the single-layer backpropagation algorithm for Gaussian input signals. It is based on a nonlinear system identification model of the desired response which is capable of generating an arbitrary hyper- plane decision boundary. It is demonstrated that, although the weights grow unbounded, the algorithm, on average, quickly learns the correct hyperplane associated with the system iden- tification model.

A discrete ARMA model for nonlinear system identification

A nonlinear extension of the discrete linear autoregressive moving average (ARMA) model is presented for the identification of nonlinear systems from measurements of input and output signals. This model is linear In the parameters and is shown to be applicable to a broad class of interconnected inear and memoryless nonlinear subsystems. Conditions for identifiability of nonlinear systems and memory requirements for the model are presented. The model contains Volterra and cross product expansions of the measured signals, which in many cases avoids the need for the large number of parameters required in a traditional Volterra expansion. It is also shown that when the model equations are recast in "regular" form, the model parameters can be obtained using multichannel lattice methods based upon the Levinson algorithm.