Nonlinear Autoregressive Moving Average Research Articles

Modeling and Identification of Rate Dependent Hysteresis in Piezoelectric Actuated Nano-Stage: A Gray Box Neural Network Based Approach

A modeling and parameter identification method for rate dependent hysteresis of piezoelectric actuated nano-stage is presented in this work. A system level quasi-static hysteresis model is employed to construct a neural network. To better describe the rate dependent behavior of hysteresis in piezoelectric actuated stage, a Nonlinear AutoRegressive Moving Average with eXogenous input (NARMAX) based dynamic model is incorporated with the quasi-static hysteresis model, where the weights of specifically designed neural network corresponds to the model parameters. To handle the multivalued problem of hysteresis, generalized input gradient is proposed to convert multivalued mapping of hysteresis into one-to-one mapping. The parameters of the nonlinear rate dependent hysteresis in piezoelectric actuated stage is identified by neural network training, taking advantage of their universal function approximation capabilities. The proposed scheme is also compared with conventional black box and particle swarm optimization identification based methods, simulation and experimental results demonstrate significant performance improvement with an error of 20.77nm for proposed method whereas 96.56nm and 31.46nm for black box and particle swarm optimization respectively.

Recurrent-neural-network-based unscented Kalman filter for estimating and compensating the random drift of MEMS gyroscopes in real time

The presence of the stochastic errors in MEMS (Micro Electro Mechanical Systems) gyroscopes makes the improvement of the measurement precision challenging. This paper addresses a novel method to estimate and compensate the random drift of MEMS gyroscopes in real time, combining unscented Kalman filter (UKF) with recurrent neural network (RNN). In the proposed method, the random drift is regarded as a generalized nonlinear autoregressive moving average (NARMA) model, and its optimal predictor is realized by a dynamic RNN. To compensate the random drift in real time, the RNN model is brought into the framework of UKF, for establishing the state equation of the improved UKF. The novelty of this paper is that a strategy is presented to guarantee the validity of the combination of UKF and RNN. The effectiveness and superiorities of the proposed method are verified by experiments.

Learning Stable Robust Adaptive NARMA Controller for UAV and Its Application to Twin Rotor MIMO Systems

This study presents a nonlinear auto-regressive moving average (NARMA) based online learning controller algorithm providing adaptability, robustness and the closed loop system stability. Both the controller and the plant are identified by the proposed NARMA based input–output models of Wiener and Hammerstein types, respectively. In order to design the NARMA controller, not only the plant but also the closed loop system identification data are obtained from the controlled plant during the online supervised learning mode. The overall closed loop model parameters are determined in suitable parameter regions to provide Schur stability. The identification and controller parameters are calculated by minimizing the $$\varepsilon $$ -insensitive error functions. The proposed controller performances are not only tested on two simulated models such as the quadrotor and twin rotor MIMO system (TRMS) models but also applied to the real TRMS with having severe cross-coupling effect between pitch and yaw. The tracking error performances of the proposed controller are observed better compared to the conventional adaptive and proportional–integral–derivative controllers in terms of the mean squared error, integral squared error and integral absolute error. The most noticeable superiority of the developed NARMA controller over its linear counterpart, namely the adaptive auto-regressive moving average (ARMA) controller, is observed on the TRMS such that the NARMA controller shows a good tracking performance not only for the simulated TRMS model but also the real TRMS. On the other hand, it is seen that the adaptive ARMA is incapable of producing feasible control inputs for the real TRMS whereas it works well for the simulated TRMS model.

Optimal Pitch Angle Control for Wind Turbine Using Intelligent Controller

Wind energy is the most plenty resource in the renewable energy purse. Increasing the wind pick out capability improves the economic viability of this technology, and makes it more rivalry with traditional fossil-fuel based supplies. Therefore, it is necessary to search control strategies that increase aerodynamic efficiency. Several controls are applied and compared during this research. The angle of blade pitch is employed to control the wind turbine (SCIG) operation during partial and full load operations, correspondingly. This work is achieved using Matlab/Simulink simulation. The effect of some compensation modules is studied such as unified power flow controllers (UPFC) and three types of smart technologies on the performance of the IEEE 9 bus. The traditional PI, is the first controller is utilized in this study that depends on trial and error technique. Second, the controller of Fuzzy logic control (FLC) based trial and error. Finally, the nonlinear auto regressive-moving average (NARMA-L2) based on PI controller. The results show that the controllers used had better improvement in active power and the response of turbine in terms of reduced error for a steady state and ripple reduction in the torque and speed responses. In addition, NARMA-L2 controller presents better results from other methods especially in power output and in terms of reducing the steady state errors of load changes and ripple minimization, making this controller more active to the load and speed variations.

Identification of Errors-in-Variables Systems with General Nonlinear Output Observations and with ARMA Observation Noises

This paper concerns the identification problem of scalar errors-in-variables (EIV) systems with general nonlinear output observations and ARMA observation noises. Under independent and identically distributed (i.i.d.) Gaussian inputs with unknown variance, recursive algorithms for estimating the parameters of the EIV systems are presented. For general nonlinear observations, conditions on the system are imposed to guarantee the almost sure convergence of the estimates. A simulation example is included to justify the theoretical results.

Evaluation of Nonlinear System Identification to Model Piezoacoustic Transmission

Piezoeletric materials are used on high-precision and high-dynamics applications, such as for acoustic transmission. This paper covers the challenges of creating a black-box model for a simultaneous acoustic transmission problem, with data acquired in a laboratory setup. The system performance is analyzed for three different models: AutoRegressive Moving Average with eXogenous inputs (ARMAX) model, Nonlinear AutoRegressive with eXogenous inputs (NARX) model with artificial neural network structure, and Nonlinear AutoRegressive Moving Average with eXogenous inputs (NARMAX) models. The best results of each models are compared with respect to precision in free-run simulation. The prediction results show that the most complex NARMAX model had the best results, what encourages further research in creating nonlinear mathematical data-driven abstractions for the piezoacoustic transmission application.

Simulation and Control of Photovoltaic Panel Using Nonlinear Autoregressive Moving Average (NARMA Controller)

Recently, the photovoltaics (PVs) is considers as one of important renewable energy systems. Generally, The PVs cell is detecting the solar radiation and converted it into a power electric DC current. In this paper, the PV has designed to produce power electrical of certain power and it has given that power with standard temperatures conditions designed at (1000 W/m2, 25 °C) for temperature and solar radiation. In case of increase or decrease in the temperature values and solar radiation the power value will be reduced. Besides, the control systems has utilized to control the power value that effected by the radiation and temperature of the PV system. An artificial neural network (ANN) technique which is nonlinear autoregressive moving average (NARMA) has used to the purpose of get the high efficiency and controlling the maximum power point (MPP) at different conditions of radiation and temperature. This control will be carried out by applying a PV model using the equivalent circuit of the PV. MATLAB-based modelling will be used for simulation and compared between results before and after using NARMA controller.

Modeling of Intelligent Control System for Liquid Level in Multi-Stage Separator Arrangement in Oil and Natural Gas Industry

The control of liquid level in the oil and natural gas industry is a very important subject since it affects the shutdown of the sale and transport of these sensitive products. In the oil separator, because of the mixing of the accompanied water, oil and accompanied gas, therefore, the level of oil must not be exceed a such rang as well as not to be less than a proper level. For this reason, this work is focused in modeling a Simulink and mathematical model for multi-stage oil separator structure and applies the intelligent schemes in order to control the angles of most inlet and outlet valves at the same time. This technique will improve the behavior of the level response in terms of the rise time, maximum present overshoot, settling time and steady state error. Also, a comparison has been implemented between (fuzzy logic, Nonlinear Autoregressive-Moving Average (NARMA-L2)) against conventional control methods such as PID control. Faster response for most oil separator can be achieved as it appears from the simulation results. Also, multi input variable that affect the system outputs can be treated accurately by a proper rule base adjusting in fuzzy logic or adequate training data in the NARMA-L2. The effective factors of fuzzy logic and NARMA-L2 had been optimized and studied where the simulation results had demonstrated that there are special magnitudes for each new application

COMPARATIVE ANALYSIS ON NONLINEAR MODELS FOR RON GASOLINE BLENDING USING NEURAL NETWORKS

The blending process always being a nonlinear process is difficult to modeling, since it may change significantly depending on the components and the process variables of each refinery. Different components can be blended depending on the existing stock, and the chemical characteristics of each component are changing dynamically, they all are blended until getting the expected specification in different properties required by the customer. One of the most relevant properties is the Octane, which is difficult to control in line (without the component storage). Since each refinery process is quite different, a generic gasoline blending model is not useful when a blending in line wants to be done in a specific process. A mathematical gasoline blending model is presented in this paper for a given process described in state space as a basic gasoline blending process description. The objective is to adjust the parameters allowing the blending gasoline model to describe a signal in its trajectory, representing in neural networks extreme learning machine method and also for nonlinear autoregressive-moving average (NARMA) in neural networks method, such that a comparative work be developed.

Modeling of a distillation column based on NARMAX and Hammerstein models

The modeling of distillation column process is a very challenging problem because of the complex dynamic behavior. This paper investigates a Nonlinear Autoregressive Moving Average with eXogenous input (NARMAX) model, and a Hammerstein model to approximate the evolution of the overhead temperature in a separation system. The model development and validation are studied through experiments carried out on a distillation plant of laboratory scale. Three model order selection criteria such as Aikeke’s Information Criterion (AIC), Root Mean Square Error (RMSE) and Nash–Sutcliffe Efficiency (NSE) are used to evaluate the prediction performance of the process behavior. The results illustrate that both models produce acceptable predictions but the NARMAX model outperforms the Hammerstein model.

Forecasting Conditional Variance of S&P100 Returns Using Feedforward and Recurrent Neural Networks

It is shown that time series about financial market variables are highly nonlinearly dependent on time. Fluctuations or volatility of returns on assets is one of them. Portfolio managers, option traders and market makers are all interested in volatility forecasting in order to get higher profits and less risky positions. The nonlinear dependence on time is very complex and parametric approaches, and linear models fail. Therefore as nonparametric tools artificial neural networks (ANNs) are candidates to deal with the volatility and/or return forecasting problems. On the other hand, based on the fact that volatility is time varying and that periods of high volatility tend to cluster, the most popular models in modeling volatility are GARCH type models because they can account excess kurtosis and asymmetric effects of financial time series. A standard GARCH(1,1) model usually indicates high persistence in the conditional variance, which may originate from structural changes. Hence it is natural that artificial neural networks (ANN) will be constructed to capture the nonlinear relationship between past return innovations and conditional variance which may be missed by linear regression models. First a usual feedforward, back propagation network is used. The structure of the return data makes FFANN difficult to converge. To overcome this difficulty a neural network with appropriate recurrent connections in the context of nonlinear ARMA models are used. These are the Jordan neural networks (JNN). Then Elman recurrent networks (ENN) and a mixture of the two (EJNN) are also used. The data set consists of returns of the S&P100 index daily closing prices obtained from the S&P100 website. The results indicate that the selected JNN(1,1,1) model has superior performances compared to the standard GARCH(1,1) model. The contribution of this paper can be seen in determining the appropriate NN that is comparable to the standard GARCH(1,1) model and its application in forecasting conditional variance of stock returns. Moreover, from the econometric perspective, NN models are used as a semi-parametric method that combines flexibility of nonparametric methods and the interpretability of parameters of parametric methods.

The Performance of Binary Artificial Bee Colony (BABC) in Structure Selection of Polynomial NARX and NARMAX Models

This paper explores the capability of the Binary Artificial Bee Colony (BABC) algorithm for feature selection of Nonlinear Autoregressive Moving Average with Exogenous Inputs (NARMAX) model, and compares its implementation with the Binary Particle Swarm Optimization (BPSO) algorithm. A binarized modification of the BABC algorithm was used to perform structure selection of the NARMAX model on a Flexible Robot Arm (FRA) dataset. The solution quality and convergence was compared with the BPSO optimization algorithm. Fitting and validation tests were performed using the One-Step Ahead (OSA), correlation and histogram tests. BABC was able to outperform BPSO in terms of convergence consistency with equal solution quality. Additionally, it was discovered that BABC was less prone to converge to local minima while BPSO was able to converge faster. Results from this study showed that BABC was better-suited for structure selection in huge dataset and the convergence has been proven to be more consistent relative to BPSO.

Comparative Analysis of Various Control Strategies for a Nonlinear CSTR System

Abstract Continuous stirred tank reactor (CSTR) is a highly nonlinear process particularly when chemical reaction takes place. The heat energy will be either liberate or absorbed by the reactor due to the reaction. The control of temperature for this process is a real challenge due to nonlinear temperature changes during reaction. In this paper a mathematical model of CSTR with its transfer function is taken for controller design and analysis. The temperature inside the reactor is controlled by altering the coolant jacket temperature. This paper compares the performances of the proportional integral derivative controller (PID) controller, PID-based nonlinear autoregressive moving average (NARMA) controller and fuzzy-based PID controller. The proposed PID-based NARMA controller shows better control of temperature than the conventional PID controller. The fuzzy-based PID controller also shows a reasonable optimal performance.

Split FTDNN-DFE Equalizer for Complex Non-linear Wireless Channels with NARMA Approximation

AbstractTime-dependent channel variations in wireless systems have been modeled using autoregressive (AR), moving average, and AR moving average (ARMA) approaches, which in certain conditions fail to provide the most suitable description of the scenarios. It lowers the quality of service, increases the dependence on the traditional tapped delay line model, and requires more reference symbols as fading in the channel increases. Non-linear attributes in channels are best described by non-linear AR (NAR) and non-linear ARMA (NARMA) models, which capture the channel state information (CSI) better. Learning-based systems like artificial neural networks (ANN) are better equipped to deal with NAR and NARMA approximations of channels, recover CSI, and provide proper channel estimation due to their natural association with non-linear computing. Though decision feedback equalizers (DFE) are the traditional and preferred approaches to reduce the ill effects of channel-induced variations, these are unable to mitigate noise-triggered responses that ANNs can. Here, DFEs and special forms of ANNs are combined to recover CSI from NAR and NARMA approximations of time-varying channels. We especially configure a class of fully focused time delay neural network designed in split form in unitary and composite modes with a DFE to track real and imaginary components of signals. Experimental results establish the effectiveness of such hybrid tools in tracking time-varying non-linear channels covering International Telecommunication Union pedestrian to vehicular conditions.

Nonlinear Mobile Link Adaptation Using Modified FLNN and Channel Sounder Arrangement

In a typical mobile environment, the varying speeds of transmit–receive pairs make traditional channel estimation methods inefficient due to continuously altering requirement of high density reference symbols. It has been largely instrumental in driving efforts to formulate innovative solutions, which are appropriate for such situations. Previously, with high computational cost, autoregressive moving average (ARMA) models of the stochastic wireless channels though appeared to be effective but could not efficiently incorporate the true nonlinearities observed in a practical situation. Therefore, nonlinear ARMA models based on artificial neural networks gained popularity. Yet certain challenges continue to exist, which are related to approximating all aspects of a real time situation, encompassing the non-linearities observed in a stochastic wireless channel, reducing training latency, enhancing processing capability, and deriving appropriate neuro-computational topologies. Modified functional link neural network with linearized activation function (FLNNLA) with nonlinear functional expansion is found to be more suitable for modeling stochastic wireless channels and removing the above-mentioned shortcomings. The proposed FLNNLA models the nonlinear tap gain process efficiently, reduces computational complexity, and enhances receiver performance with less learning cycles, better spectral efficiency and emerges as a strong candidate for being a part of upcoming receiver designs.

Distributed Reservoir Computing with Sparse Readouts [Research Frontier

In a network of agents, a widespread problem is the need to estimate a common underlying function starting from locally distributed measurements. Real-world scenarios may not allow the presence of centralized fusion centers, requiring the development of distributed, message-passing implementations of the standard machine learning training algorithms. In this paper, we are concerned with the distributed training of a particular class of recurrent neural networks, namely echo state networks (ESNs). In the centralized case, ESNs have received considerable attention, due to the fact that they can be trained with standard linear regression routines. Based on this observation, in our previous work we have introduced a decentralized algorithm, framed in the distributed optimization field, in order to train an ESN. In this paper, we focus on an additional sparsity property of the output layer of ESNs, allowing for very efficient implementations of the resulting networks. In order to evaluate the proposed algorithm, we test it on two well-known prediction benchmarks, namely the Mackey-Glass chaotic time series and the 10th order nonlinear auto regressive moving average (NARMA) system.

Binary Particle Swarm Optimization Structure Selection of Nonlinear Autoregressive Moving Average with Exogenous Inputs (NARMAX) Model of a Flexible Robot Arm

The Nonlinear Auto-Regressive Moving Average with Exogenous Inputs (NARMAX) model is a powerful, efficient and unified representation of a variety of nonlinear models. The model’s construction involves structure selection and parameter estimation, which can be simultaneously performed using the established Orthogonal Least Squares (OLS) algorithm. However, several criticisms have been directed towards OLS for its tendency to select excessive or sub-optimal terms leading to nonparsimonious models. This paper proposes the application of the Binary Particle Swarm Optimization (BPSO) algorithm for structure selection of NARMAX models. The selection process searches for the optimal structure using binary bits to accept or reject the terms to form the reduced regressor matrix. Construction of the model is done by first estimating the NARX model, then continues with the estimation of the MA model based on the residuals produced by NARX. One Step Ahead (OSA) prediction, Mean Squared Error (MSE) and residual histogram analysis were performed to validate the model. The proposed optimization algorithm was tested on the Flexible Robot Arm (FRA) dataset. Results show the success of BPSO structure selection for NARMAX when applied to the FRA dataset. The final NARMAX model combines the NARX and MA models to produce a model with improved predictive ability compared to the NARX model.

Data-based stochastic model reduction for the Kuramoto–Sivashinsky equation

The problem of constructing data-based, predictive, reduced models for the Kuramoto–Sivashinsky equation is considered, under circumstances where one has observation data only for a small subset of the dynamical variables. Accurate prediction is achieved by developing a discrete-time stochastic reduced system, based on a NARMAX (Nonlinear Autoregressive Moving Average with eXogenous input) representation. The practical issue, with the NARMAX representation as with any other, is to identify an efficient structure, i.e., one with a small number of terms and coefficients. This is accomplished here by estimating coefficients for an approximate inertial form. The broader significance of the results is discussed.

Electron flux models for different energies at geostationary orbit

Forecast models were derived for energetic electrons at all energy ranges sampled by the third-generation Geostationary Operational Environmental Satellites (GOES). These models were based on Multi-Input Single-Output Nonlinear Autoregressive Moving Average with Exogenous inputs methodologies. The model inputs include the solar wind velocity, density and pressure, the fraction of time that the interplanetary magnetic field (IMF) was southward, the IMF contribution of a solar wind-magnetosphere coupling function proposed by Boynton et al. (2011b), and the Dst index. As such, this study has deduced five new 1 h resolution models for the low-energy electrons measured by GOES (30–50 keV, 50–100 keV, 100–200 keV, 200–350 keV, and 350–600 keV) and extended the existing >800 keV and >2 MeV Geostationary Earth Orbit electron fluxes models to forecast at a 1 h resolution. All of these models were shown to provide accurate forecasts, with prediction efficiencies ranging between 66.9% and 82.3%.

System identification of smart buildings under ambient excitations

This paper proposes a nonlinear autoregressive moving average (NARMA) model for use in system identification (SI) of high performance smart buildings under ambient excitations. The NARMA model is implemented by including the cross terms of output signals to a linear autoregressive moving average (LARMA) time series model. To demonstrate the effectiveness of the proposed NARMA approach, a three-story building equipped with smart control devices is investigated under a variety of ambient excitations. To access the robustness of the proposed model, it is tested under various levels of measurement noises. It is demonstrated from the extensive simulations that the proposed NARMA model is effective in predicting the ambient vibration responses of the high performance smart buildings with severe measurement noises.