Nonlinear Autoregressive Moving Average Research Articles

Quantifying heterogeneous responses of fish community size structure using novel combined statistical techniques.

To understand changes in ecosystems, the appropriate scale at which to study them must be determined. Large marine ecosystems (LMEs) cover thousands of square kilometres and are a useful classification scheme for ecosystem monitoring and assessment. However, averaging across LMEs may obscure intricate dynamics within. The purpose of this study is to mathematically determine local and regional patterns of ecological change within an LME using empirical orthogonal functions (EOFs). After using EOFs to define regions with distinct patterns of change, a statistical model originating from control theory is applied (Nonlinear AutoRegressive Moving Average with eXogenous input – NARMAX) to assess potential drivers of change within these regions. We have selected spatial data sets (0.5° latitude × 1°longitude) of fish abundance from North Sea fisheries research surveys (spanning 1980–2008) as well as of temperature, oxygen, net primary production and a fishing pressure proxy, to which we apply the EOF and NARMAX methods. Two regions showed significant changes since 1980: the central North Sea displayed a decrease in community size structure which the NARMAX model suggested was linked to changes in fishing; and the Norwegian trench region displayed an increase in community size structure which, as indicated by NARMAX results, was primarily linked to changes in sea‐bottom temperature. These regions were compared to an area of no change along the eastern Scottish coast where the model determined the community size structure was most strongly associated to net primary production. This study highlights the multifaceted effects of environmental change and fishing pressures in different regions of the North Sea. Furthermore, by highlighting this spatial heterogeneity in community size structure change, important local spatial dynamics are often overlooked when the North Sea is considered as a broad‐scale, homogeneous ecosystem (as normally is the case within the political Marine Strategy Framework Directive).

Anomaly Detection of Network Traffic Based on Prediction and Self-Adaptive Threshold

Security problems with network are significant, such as network failures and malicious attacks. Monitoring network traffic and detect anomalies of network traffic is one of the effective manner to ensure network security. In this paper, we propose a hybrid method for network traffic prediction and anomaly detection. Specifically, the original network traffic data is decomposed into high-frequency components and low-frequency components. Then, non-linear model Relevance Vector Machine (RVM) model and ARMA (Auto Regressive Moving Average) model are employed respectively for prediction. After combining the prediction, a self-adaptive threshold method based on Central Limit Theorem (LCT) is introduced for anomaly detection. Moreover, our extensive experiments evaluate the efficiency of proposed method.

Recurrent-Neural-Network-Based Multivariable Adaptive Control for a Class of Nonlinear Dynamic Systems With Time-Varying Delay.

At the beginning, an approximate nonlinear autoregressive moving average (NARMA) model is employed to represent a class of multivariable nonlinear dynamic systems with time-varying delay. It is known that the disadvantages of robust control for the NARMA model are as follows: 1) suitable control parameters for larger time delay are more sensitive to achieving desirable performance; 2) it only deals with bounded uncertainty; and 3) the nominal NARMA model must be learned in advance. Due to the dynamic feature of the NARMA model, a recurrent neural network (RNN) is online applied to learn it. However, the system performance becomes deteriorated due to the poor learning of the larger variation of system vector functions. In this situation, a simple network is employed to compensate the upper bound of the residue caused by the linear parameterization of the approximation error of RNN. An e -modification learning law with a projection for weight matrix is applied to guarantee its boundedness without persistent excitation. Under suitable conditions, the semiglobally ultimately bounded tracking with the boundedness of estimated weight matrix is obtained by the proposed RNN-based multivariable adaptive control. Finally, simulations are presented to verify the effectiveness and robustness of the proposed control.

Output feedback adaptive control of a class of nonlinear discrete-time systems with unknown control directions and preceded by hysteresis

This paper considers the output feedback adaptive controller design problem for a class of discrete-time nonlinear systems in output feedback form with unknown control directions and preceded by unknown hysteresis. The problem of lacking in a-priori knowledge on the control directions and unknown hysteresis are solved by using the discrete Nussbaum gain and Prandtl–Ishlinskii model, respectively. The system is transformed into the form of a nonlinear auto regressive moving average (NARMA) model to construct an output feedback control. To overcome the noncausal problem in the control design, future output prediction laws and parameter update laws with the dead-zone technique are constructed on the basis of the NARMA model. The proposed control algorithm guarantees that all the signals in the controlled system are bound and the output tracking error is made to be neighbourhood around zero, ultimately. Finally, simulations are performed on a nonlinear system to show the effectiveness of the proposed method

GARCH based artificial neural networks in forecasting conditional variance of stock returns

Portfolio managers, option traders and market makers are all interested in volatility forecasting in order to get higher profits or less risky positions. Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most popular models in modelling 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. The first objective of this paper is to develop a parsimonious neural networks (NN) model, which can capture the nonlinear relationship between past return innovations and conditional variance. Therefore, the goal is to develop a neural network with an appropriate recurrent connection in the context of nonlinear ARMA models, i.e., the Jordan neural network (JNN). The second objective of this paper is to determine if JNN outperforms the standard GARCH model. Out-of-sample forecasts of the JNN and the GARCH model will be compared to determine their predictive accuracy. The data set consists of returns of the CROBEX index daily closing prices obtained from the Zagreb Stock Exchange. 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.

Recurrent support vector regression for a non-linear ARMA model with applications to forecasting financial returns

Motivated by recurrent neural networks, this paper proposes a recurrent support vector regression (SVR) procedure to forecast nonlinear ARMA model based simulated data and real data of financial returns. The forecasting ability of the recurrent SVR based ARMA model is compared with five competing models (random walk, threshold ARMA model, MLE based ARMA model, recurrent artificial neural network based ARMA model and feed-forward SVR based ARMA model) by using two forecasting accuracy evaluation metrics (NSME and sign) and robust Diebold---Mariano test. The results reveal that for one-step-ahead forecasting, the recurrent SVR model is consistently better than the benchmark models in forecasting both the magnitude and turning points, and statistically improves the forecasting performance as opposed to the usual feed-forward SVR.

Bioreactor profile control by a nonlinear auto regressive moving average neuro and two degree of freedom PID controllers

This paper presents the use of nonlinear auto regressive moving average (NARMA) neuro controller for temperature control and two degree of freedom PID (2DOF-PID) for pH and dissolved oxygen (DO) of a biochemical reactor in comparison with the industry standard anti-windup PID (AWU-PID) controllers. The process model of yeast fermentation described in terms of temperature, pH and dissolved oxygen has been used in this study. Nonlinear auto regressive moving average (NARMA) neuro controller used for temperature control has been trained by Levenberg–Marquardt training algorithm. The 2DOF-PID controllers used for pH and dissolved oxygen have been tuned by MATLAB's auto tune feature along with manual tuning. Random training data with input varying from 0 to 100l/h have been obtained by using NARMA graphical interface. The data samples used for training, validation and testing are 20,000, 10,000 and 10,000 respectively. Random profiles have been used for simulation. The NARMA neuro controller and the 2DOF-PID controllers have shown improvement in rise time, residual error and overshoot. The proposed controllers have been implemented on TMS320 Digital Signal Processing board using code composure studio. Arduino Mega board has been used for input/output interface.

Maximum likelihood gradient-based iterative estimation algorithm for a class of input nonlinear controlled autoregressive ARMA systems

This paper considers the parameter estimation problem for an input nonlinear controlled autoregressive ARMA model. The basic idea is to combine the maximum likelihood principle and the gradient search and to present a maximum likelihood gradient-based iterative estimation algorithm. The analysis and simulation results show that the proposed algorithm can effectively estimate the parameters of the input nonlinear controlled autoregressive ARMA systems.

Adaptive predictive control of periodic non‐linear auto‐regressive moving average systems using nearest‐neighbour compensation

Many practical non-linear systems can be described by non-linear auto-regressive moving average (NARMA) system models, whose stabilisation problem is challenging in the presence of large parametric uncertainties and non-parametric uncertainties. In this work, to address this challenging problem for a wide class of discrete-time NARMA systems, in which there are uncertain periodic parameters as well as uncertain non-linear part with unknown periodic time delays, we develop adaptive predictive control laws using the key ideas of `future outputs prediction' and `nearest-neighbour compensation', among which the former is carried out to overcome the non-causalness problem and the latter novel idea is proposed to completely compensate for the effect of non-linear uncertainties as well as unknown time delays. To achieve the desired asymptotic tracking performance in the presence of semi-parametric uncertainties with time delays, an ` n -step parameter update law' is first designed, based on which an `one-step update law' is then elaborately constructed to obtain smoother closed-loop signals. This study in general develops a systematic adaptive control framework for periodic NARMA systems with guaranteed boundedness stability and asymptotic tracking performance, which are established by rigorous theoretic proof and verified by simulation studies.

MPPT control design and performance improvements of a PV generator powered DC motor-pump system based on artificial neural networks

This paper presents the optimum photovoltaic (PV) water pumping system using maximum power point tracking technique (MPPT). The optimum is suspended to reference optimal power. This optimal technique is developed to assure the optimum chopping ratio of buck–boost converter. The presented MPPT technique is used in photovoltaic water pumping system in order to optimize its efficiency. An adaptive controller with emphasis on Nonlinear Autoregressive Moving Average (NARMA) based on artificial neural networks approach is applied in order to optimize the duty ratio for PV maximum power at any irradiation level. In this application, an indirect data-based technique is taken, where a model of the plant is identified on the basis of input–output data and then used in the model-based design of a neural network controller. The proposed controller has the advantages of fast response and good performance. The PV generator DC motor pump system with the proposed controller has been tested through a step change in irradiation level. Simulation results show that accurate MPPT tracking performance of the proposed system has been achieved. Further, the performance of the proposed artificial neural network (ANN) controller is compared with a PID controller through simulation studies. Obtained results demonstrate the effectiveness and superiority of the proposed approach.

Maximum Power Point Tracker Control Design of a Photovoltaic-Generator Powered DC Motor-Pump System Based on Artificial Neural Networks

This paper presents the optimisation of a photovoltaic (PV) water pumping system using maximum power point tracker (MPPT) technique. The optimisation is suspended to reference optimal power. This optimisation technique is developed to assure the optimum chopping ratio of buck-boost converter. The presented MPPT technique is used in PV water pumping system in order to optimise its efficiency. An adaptive controller with emphasis on non-linear autoregressive moving average (NARMA) based on artificial neural networks approach is applied in order to optimise the duty ratio for PV maximum power at any irradiation level. In this application, an indirect data-based technique is taken, where a model of the plant is identified on the basis of input-output data and then used in the model-based design of a neural network controller. The proposed controller has the advantages of robustness, fast response and good performance. The PV generator DC motor pump system with the proposed controller has been tested through a step change in irradiation level. Simulation results show that accurate MPPT tracking performance of the proposed system has been achieved. Further, the performance of the proposed artificial neural network (ANN) controller is compared with a proportional-integral-derivative controller through simulation studies. Obtained results demonstrate the effectiveness and superiority of the proposed approach.

Modeling, analysis and neural MPPT control design of a PV-generator powered dc motor-pump system

This paper presents the optimization of a photovoltaic (PV) water pumping system using maximum power point tracking technique (MPPT). The optimization is suspended to reference optimal power. This optimization technique is developed to assure the optimum chopping ratio of buck-boost converter. The presented MPPT technique is used in photovoltaic water pumping system in order to optimize its efficiency. An adaptive controller with emphasis on Nonlinear Autoregressive Moving Average (NARMA) based on artificial neural networks approach is applied in order to optimize the duty ratio for PV maximum power at any irradiation level. In this application, an indirect data-based technique is taken, where a model of the plant is identified on the basis of input-output data and then used in the model-based design of a neural network controller. The proposed controller has the advantages of robustness, fast response and good performance. The PV generator DC motor pump system with the proposed controller has been tested through a step change in irradiation level. Simulation results show that accurate MPPT tracking performance of the proposed system has been achieved. Further, the performance of the proposed artificial neural network (ANN) controller is compared with a PID controller through simulation studies. Obtained results demonstrate the effectiveness and superiority of the proposed approach.

PERFORMANCE IMPROVEMENT OF A PHOTOVOLTAIC GENERATOR POWERED DC MOTOR-PUMP SYSTEM BASED ON ARTIFICIAL NEURAL NETWORKS

This paper presents the optimization of a photovoltaic (PV) waterpumping system using maximum power point tracking technique(MPPT). The optimization is suspended to reference optimal power. Thisoptimization technique is developed to assure the optimum choppingratio of buck-boost converter. The presented MPPT technique is used inphotovoltaic water pumping system in order to optimize its efficiency. Anadaptive controller with emphasis on Nonlinear Autoregressive MovingAverage (NARMA) based on artificial neural networks approach isapplied in order to optimize the duty ratio for PV maximum power at anyirradiation level. In this application, an indirect data-based technique istaken, where a model of the plant is identified on the basis of inputoutputdata and then used in the model-based design of a neural networkcontroller. The proposed controller has the advantages of robustness,fast response and good performance. The PV generator DC motor pump system with the proposed controller has been tested through a step change in irradiation level. Simulation results show that accurate MPPTtracking performance of the proposed system has been achieved.Further, the performance of the proposed artificial neural network(ANN) controller is compared with a PID controller through simulationstudies. Obtained results demonstrate the effectiveness and superiority ofthe proposed approach.

FPGA Implementation of a Real-Time NARMA-Based Digital Adaptive Predistorter

This paper presents the design of a nonlinear autoregressive moving average (NARMA) digital adaptive predistorter (DAPD) for power amplifier (PA) linearization consisting of a low-complex closed-loop architecture. Both the predistortion function and the adaptation algorithm are fully implemented in a field-programmable gate array (FPGA) device, without the need for using any additional coprocessor. The proposed predistortion architecture is capable to compensate for both the PA nonlinear distortion and memory effects. Moreover, this DAPD allows almost real-time adaptation without interrupting the normal transmission. The computational complexity introduced by this DAPD is studied in this paper. The proposed theoretical design is implemented in an FPGA, whereas the linearization performance of the DAPD is validated through simulated and experimental results.

The stationarity and invertibility of a class of nonlinear ARMA models

We investigate some probabilistic properties of a new class of nonlinear time series models. A suffcient condition for the existence of a unique causal, strictly and weakly stationary solution is derived. To understand the proposed models better, we further discuss the moment structure and obtain some Yule-Walker difference equations for the second and third order cumulants, which can also be used for identification purpose. A suffcient condition for invertibility is also provided.

Data based quest for solar wind‐magnetosphere coupling function

The NARMAX (Nonlinear Autoregressive Moving Average with eXogenous inputs) modeling based approach is used to identify the relations for Solar wind Magnetosphere Coupling Functions in order to identify the one with the best Dst index forecasting abilities. It is argued that the Error Reduction Ratio which is a cornerstone concept in the NARMAX system identification methodology is more appropriate for such nonlinear system as the terrestrial magnetosphere than correlation function analysis which has often been used in the past. It is shown that the identified relationships for coupling functions are proportional to , where is the clock angle, and not to as was suggested in earlier studies. It is shown that the factor appears naturally within the analytical model of Kan and Lee (1979) as the dependence on the clock angle.

A NEW MATHEMATICAL APPROACH FOR DETECTION OF ACTIVE AREA IN HUMAN BRAIN fMRI USING NONLINEAR MODEL

Functional magnetic resonance imaging (fMRI) is widely-used for detection of the brain's neural activity. The signals and images acquired through this imaging technique demonstrate the human brain's response to pre-scheduled tasks. Several studies on blood oxygenation level-dependent (BOLD) signal responses demonstrate nonlinear behavior in response to a stimulus. In this paper we propose a new mathematical approach for modeling BOLD signal activity, which is able to model nonlinear and time variant behaviors of this physiological system. We employ the Nonlinear Auto Regressive Moving Average (NARMA) model to describe the mathematical relationship between output signals and predesigned tasks. The model parameters can be used to distinguish between rest and active states of a brain region. We applied our proposed method for active region detection on real as well as simulated data sets. The results show superior performance in comparison with existing methods.

Choosing the parameters of the NARMA model implemented with the recurrent perceptron for speech prediction

Speech signals have statistically nonstationary properties and cannot be processed properly by means of classical linear parametric models (AR, MA, ARMA). The neural network approach to time series prediction is suitable for learning and recognizing the nonlinear nature of the speech signal. We present a neural implementation of the NARMA model (nonlinear ARMA) and test it on a class of speech signals, spoken by both men and women in different dialects of the English language. The Akaike’s information criterion is proposed for the selection of the parameters of the NARMA model.

A note on the invertibility of nonlinear ARMA models

We review the concepts of local and global invertibility for a nonlinear auto-regressive moving-average (NLARMA) model. Under very general conditions, a local invertibility analysis of an NLARMA model shows the generic dichotomy that the innovation reconstruction errors either diminish geometrically fast or grow geometrically fast. We derive a simple sufficient condition for an NLARMA model to be locally invertible. The invertibility of the polynomial MA models is revisited. Moreover, we show that the threshold MA models may be globally invertible even though some component MA models are non-invertible. One novelty of our approach is its cross-fertilization with dynamical systems.

Advances in method of time-varying linear/nonlinear structural system identification and parameter estimate

The advances in methods of estimating modal parameters of a linear time-varying structural system and identifying dynamics characteristic of nonlinear time invariant structural systems in recent years are briefly reviewed. A parameter estimated procedure for linear time-varying structural system based on the subspace technology and nonlinear system identification method including scheme based on the neural networks and time varying NARMA (nonlinear auto regressive moving average) model is summarized in detail. Finally, major issues and directions for future work are discussed.