Nonlinear System Identification Research Articles

Domain adversarial neural network-based nonlinear system identification for helicopter transmission system

Domain adversarial neural network-based nonlinear system identification for helicopter transmission system

Dynamic modeling of Boiler drum using nonlinear system identification approach

Thermal power generation plays a major role in meeting present-day power demands. Efficient and economic controls of crucial elements like steam boiler section need superior control mechanism to ensure better efficiency. Identification of model, dynamics is a formidable task due to the strong coupling of process variables, nonlinearities in the dynamics and constraints on the control inputs. This paper presents the application of nonlinear modeling techniques to estimate boiler drum dynamics in terms of nonlinear model framework which is one of the important requirements for the design of drum water level controls schemes. The historical plant data for estimation is collected from boiler of 210 MW, Stage-II, Boiler-4 of Dr. Narla Tata Rao Thermal power Corporation (NTTPC) Ibrahimpatnam, Vijayawada. Different operating conditions are selected to estimate the nonlinear dynamics of the boiler to check with the existing Hammerstein, Wiener, model frame works. Later the nonlinear framework is modified to estimate other nonlinearities present in the system. The estimated model responses are presented to check the boiler dynamics.

Exergy Analysis of a Passive Thermal System Using Hammerstein–Wiener Estimation

Abstract A nonlinear system identification approach was used to exploit the nonlinearly in the exergy of the system and reduce it into two or more interconnected elements. The Hammerstein–Wiener (H-W) methodology was adopted to describe the dynamics of a passive thermal system using a combination of nonlinear and linear blocks. Here, the linear block is a discrete transfer function, which symbolizes the dynamic component of the model. The proposed model was validated using the state functions measured for the solar air collector. The mean absolute percentage error (MAPE) for enthalpy changes falls in the domain of −0.01% to 0.01%, whereas it varied from −0.06% to 0.02% as the entropy of the system changed with time. Similarly, the MAPE encountered while evaluating the exergy of the system was in the closed interval of −0.066% to −0.0017%. The average exergy gain by the H-W model across the Ist and IInd passages was, respectively, 0.90 kJ · kg−1 (8.10 g · s−1), 0.61 kJ · kg−1 (10.10 g · s−1) and 0.46 kJ · kg−1 (12.10 g · s−1); and 0.57 kJ · kg−1 (8.10 g · s−1), 0.48 kJ · kg−1 (10.10 g · s−1), and 0.79 kJ · kg−1 (12.10 g · s−1). The proposed model exhibited good fitting with the validation data.

Hybrid gray and black-box nonlinear system identification of an elastomer joint flexible robotic manipulator

Series elastic actuators possess several properties that make them widely used in collaborative robots, which play a major role in the current paradigm of industry 4.0. However, the compliant element responsible for those desired properties can also be responsible for the addition of unmodeled nonlinearities in the system. Therefore, the aim of this paper is to propose a novel hybrid model approach and apply it in the modeling of an elastomer-based series elastic joint. The proposed hybrid model combines a phenomenological gray-box model with a black-box Nonlinear Auto-regressive model with Exogenous inputs, which is able to provide the desired physical insight while enhancing accuracy by addressing the unknown nonlinearities. The results showed that the proposed hybrid model is more than 60% more accurate than the phenomenological model, considering the mean square error, and obtained a multiple correlation coefficient up to 0.97, indicating its capacity to be used in the construction of a digital twin of the system.

Recurrent general type-2 fuzzy neural networks for nonlinear dynamic systems identification

This paper introduces a recurrent general type-2 Takagi–Sugeno–Kang fuzzy neural network (RGT2-TSKFNN) for the identification of nonlinear systems. In the proposed structure, the general type-2 fuzzy set (GT2FS) and a recurrent fuzzy neural network (RFNN) are combined to obviate the data uncertainties. The fuzzy firing strengths in the developed structure are returned to the network input as internal variables. In the proposed structure, GT2FS is utilized to characterize the antecedent parts while the consequent parts are performed using TSK type. The issues of constructing a RGT2-TSKFNN involve type reduction, structure learning as well as parameter learning. An efficient strategy is developed by utilizing alpha-cuts to decompose a GT2FS into several interval type-2 fuzzy sets (IT2FSs). In order to solve the computation time of the type-reduction issue, a direct defuzzification method is used instead of iterative nature of Karnik–Mendel​ (KM) algorithm. Type-2 fuzzy clustering and Lyapunov criteria are utilized for online structure learning as well as the antecedent and consequent parameters, respectively for reducing the number of rules and guaranteeing the stability of the proposed RGT2-TSKFNN. The reported comparative analysis of the simulation results is utilized to estimate the performance of the proposed RGT2-TSKFNN with respect to other popular type-2 FNNs (T2FNNs) methodologies.

The identification of piecewise non-linear dynamical system without understanding the mechanism.

This paper designs an algorithm to distill the piecewise non-linear dynamical system from the data without prior knowledge. The system to be identified does not have to be written as a known model term or be thoroughly understood. We exploit the fact that an unknown piecewise non-linear system can be decomposed into the Fourier series as long as its equations of motion are Riemann integrable. Based on this property, we reduce the challenge of finding the correct model to discovering the Fourier series approximation. However, the Fourier series approximation of the piecewise function is inaccurate. The new method takes advantage of this weakness to determine whether the model has piecewise features and to find a way to discover the discontinuity set. Then, the dynamical system on each segment is identified as a pure Fourier series. Identification of intricate models can be achieved in simple steps. The results show that the method can accurately discover the equation of motion and precisely capture the non-smooth characteristic. Next, the prediction and further detailed analysis can be carried out.

Fractional Order Learning Methods for Nonlinear System Identification Based on Fuzzy Neural Network

Fractional Order Learning Methods for Nonlinear System Identification Based on Fuzzy Neural Network

Nonlinear System Identification Using Audio-Inspired WaveNet Deep Neural Networks

Nonlinear system identification is a challenging task that requires accurate estimation of the structural model from observations of nonlinear behavior. The WaveNet, which was originally a neural network architecture for audio processing, has been modified and first introduced to the analysis of mechanical signals to capture long-term dependencies in mechanical systems and generate high-quality signals. A novel nonlinear system identification method has been proposed using a modified WaveNet-based approach that constructs a relationship between the vibration response and the nonlinear elements in the inverse model without the need for a definite structural model. This approach uses dilated convolution for feature extraction and a multilayer perceptron for feature transition, with the addition of average pooling along the time dimension for adaptive processing of varying length data, which are more computationally efficient and widely applicable. The 13-layer modified WaveNet models have been designed and applied to the problem. Comparisons with other baseline models were made to demonstrate the method’s superiority in terms of accuracy, effectiveness, and robustness. Additionally, the method has been applied to predict composite models of friction and elastic curves, demonstrating its ability to handle diverse and complex problems.

A novel neural emulator identification of nonlinear dynamical systems using Lyapunov stability theory

This paper deals with a new weight-updating algorithm using Lyapunov stability theory (LST) for the training of a neural emulator (NE), of nonlinear systems, connected by an autonomous algorithm inspired from the real-time recurrent learning (RTRL). The proposed method is formulated by an inequality-constraint optimization problem where the Lagrange multiplier theory is used as the optimization tool. The contribution of this paper is the integration of the LST into the Lagrange constraint function to synthesize a new analytical adaptation gain rate satisfying the asymptotic stability of the NE and providing good emulation performances. To confirm the good performances and the convergence ability of the proposed adaptation algorithm, a numerical example and an experimental validation on a chemical reactor are proposed.

Variable selection and identification of high-dimensional nonparametric nonlinear systems by directional regression

Variable selection and identification of high-dimensional nonparametric nonlinear systems by directional regression

Regularised Volterra series models for modelling of nonlinear self-excited forces on bridge decks

Volterra series models are considered an attractive approach for modelling nonlinear aerodynamic forces for bridge decks since they extend the convolution integral to higher dimensions. Optimal identification of nonlinear systems is a challenging task since there are typically many unknown variables that need to be determined, and it is vital to avoid overfitting. Several methods exist for identifying Volterra kernels from experimental data, but a large class of them put restrictions on the system inputs, making them infeasible for section model tests of bridge decks. A least-squares identification method does not restrict the inputs, but the identified model often struggles with noisy (non-smooth) kernels, which is deemed to be unphysical and a sign of overfitting. In this work, regularised least-squares identification is introduced to improve the performance of model identification using least-squares. Standard Tikhonov regularisation and other penalty techniques that impose decaying kernels are also explored. The performance of the methodology is studied using experimental data from wind tunnel tests of a twin deck section. The regularised Volterra models show equal or better results in terms of modelling the self-excited forces, and the regularisation makes the models less prone to overfitting.

Parameter estimation of multiple‐input single‐output Hammerstein controlled autoregressive system based on improved adaptive moment estimation algorithm

AbstractIn this article, the problem of parameter estimation for a multiple‐input single‐output Hammerstein controlled autoregressive (MISO‐HCAR) model is solved. After establishing the identification model of MISO‐HCAR system, an improved adaptive moment estimation algorithm with decreasing weight (IADAM) is proposed. The improved algorithm transforms the nonlinear system identification problem into a parameter space optimization problem, according to the input and output data obtained from the system, and uses the parallel search ability of the IADAM algorithm to estimate all the parameters of the system simultaneously. Two numerical examples and the case study example of chemical continuously stirred tank reactor (CSTR) system show that the proposed IADAM algorithm with decreasing weight has better identification effect on the MISO‐HCAR model and CSTR system than the stochastic gradient descent (SGD) algorithm and the basic adaptive moment estimation (ADAM) algorithm, and the estimation accuracy and convergence speed are greatly improved. Thus, the IADAM can estimate the parameters of the MISO‐HCAR system and the CSTR system more effectively.

A study on data-driven identification and representation of nonlinear dynamical systems with a physics-integrated deep learning approach: Koopman operators and nonlinear normal modes

Identifying the intrinsic coordinates or modes of dynamical systems is essential to understand, analyze, and characterize the underlying complex dynamical behaviors. This is a critical challenge for nonlinear dynamical systems because the modal transformation, which is universal for linear systems, no longer applies. Koopman operators and nonlinear normal modes (NNMs) are two main frameworks aiming to provide a general representation of nonlinear dynamics. In this study, we investigate their abilities on representing nonlinear dynamical systems. Addressing the challenge that the closed-form models or equations of dynamical systems are generally unknown realistically, we first present a physics-integrated deep learning-based data-driven framework to identify the eigenfunction of Koopman operators and the nonlinear modal transformation function of NNMs, respectively. We then evaluate their representation abilities by their reconstruction and predictive accuracy of the nonlinear dynamical response using the identified Koopman modes and NNMs. We conduct numerical experiments on Duffing systems with varying nonlinearity levels and dimensions, and observe that NNMs achieve higher representation accuracy and better computational efficiency than Koopman operators using the same dimension of intrinsic coordinates or modes.

Complex systems modelling of UK winter wheat yield

Wheat is one of the most important global crops, understanding the drivers of wheat yield has significant societal benefits. Climate variables are particularly important in determining interannual variations in wheat yield, either as primary factors which directly influence the stages of wheat growth, or as secondary factors through their influence on pests, diseases and soil conditions. Here we present a new approach to model wheat yield; an empirical method based on nonlinear complex systems identification, known as NARMAX (Nonlinear AutoRegressive Moving Average with eXogenous inputs model). We deploy the NARMAX analytical approach for a specific site, Rothamsted, UK, where detailed meteorological variables are available, together with specific information on site conditions and crop growth stages. NARMAX yield forecasts are compared with those from the WOFOST crop model and nine state-of-the-art machine learning (ML) models; experimental results show that NARMAX outperforms all the compared methods in both prediction accuracy and model interpretability. We also develop regional wheat yield forecasts derived from a new gridded meteorological data product.The NARMAX approach produces skillful forecasts (r = 0.78) of Rothamsted wheat yield for a validation period, with small errors. The NARMAX regional forecasts, based on less specific information than WOFOST, also show a high degree of skill (r = 0.73). In addition, the predictor terms chosen for the model are identifiable and can help to give insight into potential key processes involved in the determination of wheat yield at a specific location. This approach can be extended in principle to other crop types and locations. It is straightforward and inexpensive to implement, using a limited number of meteorological predictor variables, which can be taken from site-based observations, or from gridded meteorological datasets. The method is a new tool to understand the environmental drivers of wheat yields on an annual basis.

Identification of Nonlinear Systems Using the Hammerstein-Wiener Model with Improved Orthogonal Functions

Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents a linear dynamic component placed between the first two blocks. Some of the common linear model structures include a rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive with extra input (ARX), autoregressive moving average with exogenous inputs model (ARMAX), and output-error (O-E) model structure. This paper presents a new structure, and a new improvement is proposed, which is consisted of the basic structure of Hammerstein-Wiener models with an improved orthogonal function of Müntz-Legendre type. We present an extension of generalised Malmquist polynomials that represent Müntz polynomials. Also, a detailed mathematical background for performing improved almost orthogonal polynomials, in combination with Hammerstein-Wiener models, is proposed. The proposed approach is used to identify the strongly nonlinear hydraulic system via the transfer function. To compare the results obtained, well-known orthogonal functions of the Legendre, Chebyshev, and Laguerre types are exploited.

Neuromodel of an Eddy Current Brake for Load Emulation

The eddy current brake (ECB) is an electromechanical energy conversion device that can be used as a load emulator to load a motor according to the intended load scenario. However, conducting an analysis in the time domain is difficult due to its complex behavior involving mechanical, electrical, and magnetic phenomena. The challenges with the time domain analysis of the ECB require new modeling approaches that provide reliability, robustness, and controllability over a wide speed interval. If the ECB can be modeled with high accuracy, it can be controlled like a load emulator that can simulate nonlinear industrial loads. This paper describes a neuromodeling approach taken to develop an ECB. The nonlinear characteristic of the brake system was modeled with a high performance by using an artificial neural network (ANN), which is a potent nonlinear system identification tool. Several characteristics of a designed and optimized brake system undergoing various excitation currents in whole speed regions are described and verified experimentally. Eventually, an electromechanical brake system is proposed that aims to provide the required linear or nonlinear load model dynamics throughout an emulation process in line with the obtained neuromodel. To identify the most suitable ANN architecture for the problem, various ANN configurations, ranging from 1 neuron to 20 neurons in the hidden layer, as well as a statistical approach that differs from the existing literature, are presented. Additionally, the suggested model’s scalability is discussed.

Hierarchical maximum likelihood identification based on Levenberg–Marquardt and particle swarm optimization for feedback nonlinear systems

This article covers the identification of the feedback nonlinear systems. The parameterized nonlinear identification model involves products of system nonlinear part parameters and system linear part parameters. To deal with these product terms, the hierarchical identification based on maximum likelihood is used to decompose the system into two subsystems. The Levenberg–Marquardt and particle swarm optimization methods are applied for identifying the two subsystems, respectively. For the purpose of enhancing the optimization capability of the basic particle swarm optimization method, some improvement strategies are constructed. Thus, the improved particle swarm optimization algorithm which combines the adaptive feedback, the linearly decreasing method and the mutational operator is applied to adaptively adjust the search strategy and improve the ergodicity. The simulation indicates that the derived estimation is effective because it can obtain high identification accuracy and fast convergence speed when identifying the feedback systems. Besides, the case study demonstrates that the proposed method can be well used to identify the electro-hydraulic-servo position system.

Data-based modeling and control of nonlinear process systems using sparse identification: An overview of recent results

This paper discusses recent developments in the data-based modeling and control of nonlinear chemical process systems using sparse identification of nonlinear dynamics (SINDy). SINDy is a recent nonlinear system identification technique that uses only measurement data to identify model dynamical systems in the form of first-order nonlinear differential equations. In this work, the challenges of handling time-scale multiplicities and noisy sensor data when using SINDy are addressed. Specifically, a brief overview of novel methods devised to overcome these challenges are described, along with modeling guidelines for using the proposed techniques for process systems. When applied to two-time-scale systems, to overcome model stiffness, which leads to ill-conditioned controllers, a reduced-order modeling approach is proposed where SINDy is used to model the slow dynamics, and nonlinear principal component analysis is used to algebraically “slave” the fast states to the slow states. The resulting model can then be used in a Lyapunov-based model predictive controller with guaranteed closed-loop stability provided the separation of fast and slow dynamics is sufficiently large. To handle high levels of sensor noise, SINDy is combined with subsampling and co-teaching to improve modeling accuracy. The challenges of modeling and controlling large-scale systems using noisy industrial data are then addressed by using ensemble learning with SINDy. After summarizing the advances, a nonlinear chemical process is used to provide an end-to-end demonstration of process modeling using sparse identification with guidelines for chemical engineering practitioners. Finally, several future research directions for the incorporation of SINDy into process systems engineering are proposed.

A Novel Second-OrderSine-Cost-Function-Derived Kernel Adaptive Algorithm for Non-Linear System Identification

A novel kernel recursive second-order sine adaptive (KRSOSA) algorithm was devised for identifying non-linear systems, which was constructed using a symmetry squared sine function to develop a novel kernel loss function and recursive scheme. In the proposed KRSOSA algorithm, the squared sine function provides resistance to impulsive noise due to the sine operation, which was well-derived and investigated in the framework of kernel adaptive filtering (KAF). The behavior of the proposed KRSOSA algorithm was investigated and analyzed using computer simulations, which provided good performance for identifying non-linear systems under impulsive noises.

A regularised fast recursive algorithm for fraction model identification of nonlinear dynamic systems

The fraction model has been widely used to represent a range of engineering systems. To accurately identify the fraction model is however challenging, and this paper presents a regularised fast recursive algorithm (RFRA) to identify both the true fraction model structure and the associated unknown model parameters. This is achieved first by transforming the fraction form to a linear combination of nonlinear model terms. Then the terms in the denominator are used to form a regularisation term in the cost function to offset the bias induced by the linear transformation. According to the structural risk minimisation principle based on the new cost function, the model terms are selected based on their contributions to the cost function and the coefficients are then identified recursively without explicitly solving the inverse matrix. The proposed method is proved to have low computational complexity. Simulation results confirm the efficacy of the method in fast identification of the true fraction models for the targeted nonlinear systems.