Approach For Nonlinear System Identification Research Articles

Prediction, modelling, and forecasting of PM and AQI using hybrid machine learning

This paper proposes a combination of hybrid models like Input Variable Selection (IVS), Machine Learning (ML), and regression method to predict, model, and forecast the daily concentrations of particulate matter (PM1, PM2.5, PM10) and Air Quality Index (AQI). A sensor placed in the centre of Craiova, Romania, provides a two-year dataset for training, testing, and validation phases. The analysis identifies the most important predictor variables for PM prediction and forecasting. The coefficient of determination (R2) values in this stage exceeded 0.95 (95%), indicating a strong correlation between PM concentrations. The performance of the proposed models is evaluated by objective measures, including root mean squared error (RMSE) and standard deviation (σ). RMSE ranged between 0.65 and 1 μg/m3, while σ has values between 2.75 and 4.1 μg/m3, reflecting a high level of precision and a successful performance of the proposed models. Furthermore, 13 multivariable-based PM models are developed in this study and adjusted using a hybrid Least Square - Decision Tree approach. The R2 values for these adjusted models range from 0.66 to 0.75, while the RMSE and σ vary between 8 and 9.1 μg/m3. Finally, a handled application for multistep-ahead time series forecasting is elaborated by combining the Nonlinear System Identification (NARMAX) approach with Decision Tree machine learning. This application allows for forecasting PM concentrations and AQI for the next periods. The R2 values obtained in this stage surpass 0.93, indicating almost a high level of accuracy. The RMSE ranged between 4.43 and 6.25 μg/m3, while the σ ranged between 4.44 and 6.26 μg/m3, further validating the precision of our forecasting model.

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.

Tunable dynamics in Yoshimura origami by harnessing pneumatic pressure

The unique merits of origami structures and origami metamaterials are the folding-induced shape reconfigurability and the associated evolution of mechanical properties. However, currently, there is a lack of mature solutions on how to achieve active tuning, and the tunability is stuck in static properties. Therefore, this study proposes a pneumatic scheme to overcome the above two bottleneck problems. Specifically, by integrating a pneumatic bladder with a monostable Yoshimura-ori structure, a pneumatic Yoshimura origami (PYO) cell is designed. Compared with the conventional approach making use of the origami multistability, the pressure scheme is simpler in design, more accurate in regulation, and richer in configurations. To exploit the PYO structure for tunable dynamics, the dynamic model is developed via a nonlinear system identification approach, in which the overall system, including the structure itself and the friction contact, is represented as a nonlinear spring-damper element, with the constitutive profile identified via the weighted least square method from the dynamic experimental data. Based on the developed model, the pressure tunability is then explored in a 6-cell PYO structure and a PYO metamaterial. Through comprehensive linear dispersion analyses and numerical simulations, we reveal that pressure could effectively tune the passbands of the 6-cell structure so that the transmission of vibration, at certain frequencies, can be qualitatively switched between amplification and attenuation; from another perspective, pressure could also be tailored for programming the stopbands of the PYO metamaterial to achieve the shift between propagation and prohibition. The results of this investigation could provide useful guidelines for the development of intelligent origami structures/metamaterials with excellent tunability, and meanwhile, open a new perspective of origami dynamics research.

A Fuzzy MLP Approach for Nonlinear System Identification

In case of decision making problems, identification of nonlinear systems is an important issue. Identification of nonlinear systems using a multilayer perceptron (MLP) trained with back propagation becomes much complex with an increase in number of input data, number of layers, number of nodes, and number of iterations in computation. In this paper, an attempt has been made to use fuzzy MLP and its learning algorithm for identification of nonlinear system. The fuzzy MLP and its training algorithm which allows to accelerate a process of training, which exceeds in comparison with classical MLP is proposed. Results show a sharp reduction in search for optimal parameters of a neuro fuzzy model as compared to the classical MLP. A training performance comparison has been carried out between MLP and the proposed fuzzy-MLP model. The time and space complexities of the algorithms have been analyzed. It is observed that the number of epochs has sharply reduced and performance increased compared with classical MLP.

Prediction of Blood Glucose Level Using Nonlinear System Identification Approach

Predicting the blood glucose level of type 1 diabetes mellitus of patients could prevent hypo/hyperglycemia incidents that are threats for the patients with this disease. A nonlinear system identification approach is proposed in this work to develop a mathematical model, which can be used to predict the blood glucose level over a given period with high accuracy. More specifically, the Hammerstein Box-Jenkins model is used to approximate the system, where two infinite impulse response filters represent the linear and noise processes, and a polynomial basis function represents the nonlinearity. The proposed identification method is based on the Steiglitz-McBride approach to predict the model parameters. Moreover, a simulation software licensed by the USA Food and Drug Administration that simulates the dynamics of the glucose-insulin system metabolism inside the body, called Type I Diabetes Metabolic Simulator (T1DMS), was used to generate the data. Thirty subjects of different age groups were considered, and the data was generated for a week with a sample per minute, i.e. 302430 data points. This data was then processed using a developed MATLAB code to predict the blood glucose level. Various scenarios were established to validate the proposed approach. The simulations showed very promising results with a very low average root mean square error of 1 mg/dl, which is seven times less compared to other prediction techniques. Other cost functions have also been used and they showed very good results. In the future, this approach can be embedded in closed-loop continuous blood glucose monitoring systems in order to give alerts to the patients and help in calculating the needed insulin dose.

Airfoil buffet aerodynamics at plunge and pitch excitation based on long short-term memory neural network prediction

In the present study, a nonlinear system identification approach based on a long short-term memory (LSTM) neural network is applied for the prediction of transonic buffet aerodynamics. The identification approach is applied as a reduced-order modeling (ROM) technique for an efficient computation of time-varying integral quantities such as aerodynamic force and moment coefficients. Therefore, the nonlinear identification procedure as well as the generalization of the ROM are presented. The training data set for the LSTM–ROM is provided by performing forced-motion unsteady Reynolds-averaged Navier–Stokes simulations. Subsequent to the training process, the ROM is applied for the computation of the aerodynamic integral quantities associated with transonic buffet. The performance of the trained ROM is demonstrated by computing the aerodynamic loads of the NACA0012 airfoil investigated at transonic freestream conditions. In contrast to previous studies considering only a pitching excitation, both the pitch and plunge degrees of freedom of the airfoil are individually and simultaneously excited by means of an user-defined training signal. Therefore, strong nonlinear effects are considered for the training of the ROM. By comparing the results with a full-order computational fluid dynamics solution, a good prediction capability of the presented ROM method is indicated. However, compared to the results of previous studies including only the airfoil pitching excitation, a slightly reduced prediction performance is shown.

Highly Sensitive Nonlinear Identification to Track Early Fatigue Signs in Flexible Structures

Abstract This study describes a physics-based and data-driven nonlinear system identification (NSI) approach for detecting early fatigue damage due to vibratory loads. The approach also allows for tracking the evolution of damage in real-time. Nonlinear parameters such as geometric stiffness, cubic damping, and phase angle shift can be estimated as a function of fatigue cycles, which are demonstrated experimentally using flexible aluminum 7075-T6 structures exposed to vibration. NSI is utilized to create and update nonlinear frequency response functions, backbone curves and phase traces to visualize and estimate the structural health. Findings show that the dynamic phase is more sensitive to the evolution of early fatigue damage than nonlinear parameters such as the geometric stiffness and cubic damping parameters. A modified Carrella–Ewins method is introduced to calculate the backbone from nonlinear signal response, which is in good agreement with the numerical and harmonic balance results. The phase tracing method is presented, which appears to detect damage after approximately 40% of fatigue life, while the geometric stiffness and cubic damping parameters are capable of detecting fatigue damage after approximately 50% of the life-cycle.

Recognition of visual-related non-driving activities using a dual-camera monitoring system

For a Level 3 automated vehicle, according to the SAE International Automation Levels definition (J3016), the identification of non-driving activities (NDAs) that the driver is engaging with is of great importance in the design of an intelligent take-over interface. Much of the existing literature focuses on the driver take-over strategy with associated Human-Machine Interaction design. This paper proposes a dual-camera based framework to identify and track NDAs that require visual attention. This is achieved by mapping the driver's gaze using a nonlinear system identification approach, on the object scene, recognised by a deep learning algorithm. A novel gaze-based region of interest (ROI) selection module is introduced and contributes about a 30% improvement in average success rate and about a 60% reduction in average processing time compared to the results without this module. This framework has been successfully demonstrated to identify five types of NDA required visual attention with an average success rate of 86.18%. The outcome of this research could be applicable to the identification of other NDAs and the tracking of NDAs within a certain time window could potentially be used to evaluate the driver's attention level for both automated and human-driving vehicles.

A one-dimensional flow model enhanced by machine learning for simulation of vocal fold vibration.

A one-dimensional (1D) unsteady and viscous flow model that is derived from the momentum and mass conservation equations is described, and to enhance this physics-based model, a machine learning approach is used to determine the unknown modeling parameters. Specifically, an idealized larynx model is constructed and ten cases of three-dimensional (3D) fluid-structure interaction (FSI) simulations are performed. The flow data are then extracted to train the 1D flow model using a sparse identification approach for nonlinear dynamical systems. As a result of training, we obtain the analytical expressions for the entrance effect and pressure loss in the glottis, which are then incorporated in the flow model to conveniently handle different glottal shapes due to vocal fold vibration. We apply the enhanced 1D flow model in the FSI simulation of both idealized vocal fold geometries and subject-specific anatomical geometries reconstructed from the magnetic resonance imaging images of rabbits' larynges. The 1D flow model is evaluated in both of these setups and shown to have robust performance. Therefore, it provides a fast simulation tool that is superior to the previous 1D models.

Hammerstein Box-Jenkins System Identification of the Cascaded Tanks Benchmark System

A common process control application is the cascaded two-tank system, where the level is controlled in the second tank. A nonlinear system identification approach is presented in this work to predict the model structure parameters that minimize the difference between the estimated and measured data, using benchmark datasets. The general suggested structure consists of a static nonlinearity in cascade with a linear dynamic filter in addition to colored noise element. A one-step ahead prediction error-based technique is proposed to estimate the model. The model is identified using a separable least squares optimization, where only the parameters that appear nonlinearly in the output of the predictor are solved using a modified Levenberg–Marquardt iterative optimization approach, while the rest are fitted using simple least squares after each iteration. Finally, MATLAB simulation examples using benchmark data are included.

A Spline Kernel-Based Approach for Nonlinear System Identification with Dimensionality Reduction

This paper proposes a novel approach for identification of nonlinear systems. By transforming the data space into a feature space, kernel methods can be used for modeling nonlinear systems. The spline kernel is adopted to produce a Hilbert space. However, a problem exists as the spline kernel-based identification method cannot deal with data with high dimensions well, resulting in huge computational cost and slow estimation speed. Additionally, owing to the large number of parameters to be estimated, the amount of training data required for accurate identification must be large enough to satisfy the persistence of excitation conditions. To solve the problem, a dimensionality reduction strategy is proposed. Transformation of coordinates is made with the tool of differential geometry. The purpose of the transformation is that no intersection of information with relevance to the output will exist between different new states, while the states with no impact on the output are extracted, which are then abandoned when constructing the model. Then, the dimension of the kernel-based model is reduced, and the number of parameters to be estimated is also reduced. Finally, the proposed identification approach was validated by simulations performed on experimental data from wind tunnel tests. The identification result turns out to be accurate and effective with lower dimensions.

State-Space Kernelized Closed-Loop Identification of Nonlinear Systems

In this paper, we propose a non-parametric state-space identification approach for open-loop and closed-loop discrete-time nonlinear systems with multiple inputs and multiple outputs. Employing a least squares support vector machine (LS-SVM) approach in a reproducing kernel Hilbert space framework, a nonlinear auto-regressive model with exogenous terms is identified to provide a non-parametric estimate of the innovation noise sequence. Subsequently, this estimate is used to obtain a compatible non-parametric estimate of the state sequence in an unknown basis using kernel canonical correlation analysis. Finally, the estimate of the state sequence is used together with the estimated innovation noise sequence to find a non-parametric state-space model, again using a LS-SVM approach. The performance of the approach is analyzed in a simulation study with a nonlinear system operating both in open loop and closed loop. The identification approach can be viewed as a nonlinear counterpart of consistent subspace identification techniques for linear time-invariant systems operating in closed loop.

Two-Dimensional (2D) particle swarms for structure selection of nonlinear systems

The present study proposes a new structure selection approach for non-linear system identification based on Two-Dimensional particle swarms (2D-UPSO). The 2D learning framework essentially extends the learning dimension of the conventional particle swarms and explicitly incorporates information about the cardinality (i.e., number of terms) into the search process. This property of the 2D-UPSO is exploited to determine the correct structure of the non-linear systems. The efficacy of the proposed approach is demonstrated by considering several simulated benchmark nonlinear systems in discrete and continuous domains. In addition, the proposed approach is applied to identify a parsimonious structure from practical non-linear wave-force data. The results of the comparative investigation with four meta-heuristic algorithms and classical orthogonal forward regression methods illustrate that the proposed 2D-UPSO can successfully detect the correct structure of the non-linear systems.

Novel identification approach for nonlinear systems with hysteresis

A new identification approach for a nonlinear system with hysteresis, namely a cascading Bouc–Wen hysteresis model with linear dynamics, is proposed in this study. The properties of the Bouc–Wen model are analyzed under specific inputs. These properties play important roles in the parameter identification procedure. Unlike the commonly used iterative search or two-step identification scheme, the proposed approach completely decouples the identification tasks of linear and nonlinear parts and transforms each task into a linear task without iteration. First, a set of equations based on the aforementioned properties is developed. These equations enable the least squares estimation of all the parameters involved in linear dynamics with the use of the designed input signals and extended state estimation. Second, after the linear part is obtained, the hysteresis output is observed and used to establish the least squares estimation of all the parameters in the nonlinear part based on its input–output data. Simulation studies are performed to demonstrate the effectiveness of the proposed approach.

Linear parameter-varying systems identification with slowly sampled outputs subjected to unknown time-delays and outliers

This article proposes a robust global identification approach for nonlinear systems with slowly sampled outputs subjected to unknown time-delays. The inputs of the system are fast-rate sampled while the informative outputs are uniformly sampled at a slow rate. In practical industries, the outlier and output time-delays are commonly encountered and they are both considered in this work. To eliminate the impact brought by the outliers, the robust linear parameter-varying finite impulse response observation model based on the Laplace distribution is established. The unknown time-delay is treated as a random integer at each sampling moment which follows the uniform distribution with the boundary known a priori. The proposed robust approach is derived in the expectation-maximization algorithm scheme and the formulas to iteratively update the model parameters, the scale parameter and the random output time-delays are derived, respectively. The unmeasurable noise-free fast-rate sampled outputs are estimated by simulating the identified model. A numerical example, the mass-spring-damper system and the two-link robotic manipulator are utilized to verify the effectiveness of the proposed approach.

Identification of block-oriented nonlinear systems starting from linear approximations: A survey

Block-oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use. Many different identification approaches were developed over the years to estimate the parameters of a wide range of block-oriented nonlinear models. One class of these approaches uses linear approximations to initialize the identification algorithm. The best linear approximation framework and the ϵ-approximation framework, or equivalent frameworks, allow the user to extract important information about the system, guide the user in selecting good candidate model structures and orders, and prove to be a good starting point for nonlinear system identification algorithms. This paper gives an overview of the different block-oriented nonlinear models that can be identified using linear approximations, and of the identification algorithms that have been developed in the past. A non-exhaustive overview of the most important other block-oriented nonlinear system identification approaches is also provided throughout this paper.

Adaptive recurrent neural network with Lyapunov stability learning rules for robot dynamic terms identification

In this paper, a recurrent neural network coupled with Kalman filter is proposed to identify dynamic terms of robotic manipulator. By cooperating some inherent characteristics of robot, this network has the capability to individually identify nonlinear terms using Weighted Augmentation Error (WAE). To present the infrastructure of architecture, an adaptive scheme based on the conventional Back Propagation (BP) is firstly driven using the Gradient Descent (GD) method. Additionally, a stable adaptive updating rule is extracted from the discrete time Lyapunov candidate as an approach for the general nonlinear system identification. Then, this approach is applied to the predefined network. To experimentally validate the computational efficiency and control applicability of the proposed method, Adaptive Neural Network Based Inverse Dynamic Control (ANN-Based-IDC) is employed on a laboratory-scaled twin-rotor CE-150 helicopter. This experiment illustrates enhancement of steady-state performance from 2-to-3 times more in compared with simple PID. Moreover, disturbance rejection and robustness tests admit capability of the method for online dynamic identification in the presence of output and dynamic perturbation.

Multiple model approach for nonlinear system identification with mixed-Gaussian weighting functions

Multiple modelling strategies have been developed for industrial processes with multiple operating conditions. However, in most of the existing works, the adjacent operating points are not changed significantly. In this paper, a multiple model approach with the mixed-Gaussian weighting functions is proposed, and the mixed-Gaussian weighting functions as the probability distributions are assigned to each local model. Three different mixture weights are introduced: the mixture weights are pre-determined; the mixture weights are unknown matrix; and the mixture weights follow Gaussian distribution. Under the framework of the expectation-maximisation (EM) algorithm, the parameters of local models as well as those of the mixed-Gaussian weighting functions are estimated simultaneously. To illustrate the effectiveness of the proposed approach, a numerical example and a distillation column example are considered. Furthermore, an experimental study on a pilot-scale hybrid tank system is also provided to highlight the practical utility.

Multiple model approach for nonlinear system identification with mixed-Gaussian weighting functions

Multiple modelling strategies have been developed for industrial processes with multiple operating conditions. However, in most of the existing works, the adjacent operating points are not changed significantly. In this paper, a multiple model approach with the mixed-Gaussian weighting functions is proposed, and the mixed-Gaussian weighting functions as the probability distributions are assigned to each local model. Three different mixture weights are introduced: the mixture weights are pre-determined; the mixture weights are unknown matrix; and the mixture weights follow Gaussian distribution. Under the framework of the expectation-maximisation (EM) algorithm, the parameters of local models as well as those of the mixed-Gaussian weighting functions are estimated simultaneously. To illustrate the effectiveness of the proposed approach, a numerical example and a distillation column example are considered. Furthermore, an experimental study on a pilot-scale hybrid tank system is also provided to highlight the practical utility.