Final Prediction Error Research Articles

Modeling, system identification and design of fuzzy PID controller for discharge dynamics of metal hydride hydrogen storage bed

This paper presents the mathematical modeling of metal hydride based hydrogen storage bed. The novelty of this research work is the identification of transfer function for the dynamic discharge process of hydrogen storage bed is carried out using system identification tool box. A Fuzzy PID controller is modeled to regulate the pressure rate of hydrogen storage bed using MATLAB Simulink toolbox. The proposed controller reduces the complexity in controlling the pressure rate of hydrogen storage bed during desorption process for an adequate use in fuel cell and in other applications. To validate the reliability of the hydrogen storage bed model, the obtained results are verified with the results of other literature. The exact system transfer function model chosen is Box-Jenkin model, based on the simulated results of different black box model structures for the parameters such as percentage of fitness, final prediction error and the cost function. Usually, for the safer discharge of hydrogen gas, the classical PID controller is employed to control the pressure by manipulating the heating temperature of the storage bed. In order to have a better control, a Fuzzy-PID controller is proposed in this study. The proposed controller produces improved time domain response and better performance compared to the conventional PID controller.

Lattice-Filter-Based Multivariate Autoregressive Spectral Estimation With Joint Model Order and Estimation Bandwidth Adaptation

The problem of parametric autoregressive model-based estimation of a time-varying spectral density function of a multivariate nonstationary process is considered. It is shown that estimation results can be considerably improved if identification of the autoregressive model is carried out using the two-sided doubly exponentially weighted lattice algorithm, which combines results yielded by two one-sided lattice algorithms running forward in time and backward in time, respectively. It is also shown that the model order and the most appropriate estimation bandwidth can be efficiently selected using the suitably modified Akaike's final prediction error criterion.

Estimation of conditional mean squared error of prediction for claims reserving

AbstractThis paper studies estimation of the conditional mean squared error of prediction, conditional on what is known at the time of prediction. The particular problem considered is the assessment of actuarial reserving methods given data in the form of run-off triangles (trapezoids), where the use of prediction assessment based on out-of-sample performance is not an option. The prediction assessment principle advocated here can be viewed as a generalisation of Akaike’s final prediction error. A direct application of this simple principle in the setting of a data-generating process given in terms of a sequence of general linear models yields an estimator of the conditional mean squared error of prediction that can be computed explicitly for a wide range of models within this model class. Mack’s distribution-free chain ladder model and the corresponding estimator of the prediction error for the ultimate claim amount are shown to be a special case. It is demonstrated that the prediction assessment principle easily applies to quite different data-generating processes and results in estimators that have been studied in the literature.

Forecasting the Number of Monthly Active Facebook and Twitter Worldwide Users Using ARMA Model

In this study, an Auto-Regressive Moving Average (ARMA) Model with optimal order has been developed to estimate and forecast the short term future numbers of the monthly active Facebook and Twitter worldwide users. In order to pickup the optimal estimation order, we analyzed the model order vs. the corresponding model error in terms of final prediction error. The simulation results showed that the optimal model order to estimate the given Facebook and Twitter time series are ARMA[5, 5] and ARMA[3, 3], respectively, since they correspond to the minimum acceptable prediction error values. Besides, the optimal models recorded a high-level of estimation accuracy with fit percents of 98.8% and 96.5% for Facebook and Twitter time series, respectively. Eventually, the developed framework can be used accurately to estimate the spectrum for any linear time series.

Performance analysis of non-reflective boundary conditions on sound localization problem in an isotropic plate

Acoustic source localization, considering the effect of reflected waves from geometrical features (such as holes, lugs and structural discontinuities) is still one of the most challenging areas in this field. In this paper, the effects of reflected waves from edges on source localization results are discussed. Most of the previous studies have ignored the reflected waves by selection of the test zone far from the test plate edges. The current approaches for considering reflected waves are based on using high Sampling Rate Data (SRD) which is unsuitable for practical applications.This paper discusses how silicon dampers on edges affect the acoustic source localization on an isotropic plate using low SRD. In this approach, four silicon dampers are installed on a Plexiglas plate. The effect of each damper is experimentally tested on final prediction error. The experimental results reveal that the reduction of prediction error according to each damper highly depends on the impact and sensor location related to the damper’s position.

On Noncausal Identification of Nonstationary Multivariate Autoregressive Processes

The problem of identification of nonstationary multivariate autoregressive processes using noncausal local estimation schemes is considered and a new approach to joint selection of the model order and the estimation bandwidth is proposed. The new selection rule, based on evaluation of pseudoprediction errors, is compared with the previously proposed one, based on the modified Akaike's final prediction error criterion.

Estimation of Conditional Mean Squared Error of Prediction for Claims Reserving

This paper studies estimation of conditional mean squared error of prediction, conditional on what is known at the time of prediction. The particular problem considered is the assessment of actuarial reserving methods given data in the form of runoff triangles (trapezoids), where the use of prediction assessment based on out-of-sample performance is not an option. The prediction assessment principle advocated here can be viewed as a generalization of Akaike's final prediction error. A direct application of this simple principle in the setting of a data generating process given in terms of a sequence of general linear models yields an estimator of conditional mean square error of prediction that can be computed explicitly for a wide range of models within this model class. Mack's distribution-free chain ladder model and the corresponding estimator of the prediction error for the ultimate claim amount is shown to be a special case. It is demonstrated that the prediction assessment principle easily applies to quite different data generating processes and results in estimators that have been studied in the literature.

Assessing the impact of EI Niño southern oscillation index and land surface temperature fluctuations on dengue fever outbreaks using ARIMAX(p)-PARX(p)-NBARX(p) models

The dengue infectious disease remnants a human health problem in tropical and subtropical countries. In an Auto Regressive model to assess the role of climatic parameter El Nino Southern Oscillation and land surface mean monthly temperture on dengue outbreaks of the Karachi region over the monthly time interval January 2001 to December 2016, subsequent to stabilization of variance, we are able to apply and predict an Auto Regressive Integrated Moving Average Exogenous-Transfer Function model by using the order selection criteria namely Final Prediction Error and Akaike’s information. The results confirmed that ARIMAX (2,1,2) has fitted model, although an Auto Regressive model predicts a smaller decline in dengue data series than the auto Poisson Regression model. Additionally, we developed an alternative model for the Poisson Autoregressive Exogenous model in order (p) and Negative Binomial Auto Regressive Exogenous model, deliver the best fit as compared to the Poisson Auto Regressive Exogenous model whereas indicated by the deviances. The Pearson test showed a strong positive association between temperature and dengue, while ENSO inverse indication. High dengue outbreaks are detected in the months of September, October, and November. This comparative study exposed a significant relationship among monthly dengue and climatic variation by Auto Regressive Integrated Moving Average Exogenous (ARIMAX), Poisson and Negative-Binomial Autoregressive Exogenous (PARX-NBARX) models, while smallest values of AIC (3.89), Negative Binomial Auto Regressive Exogenous, are preferred more accurate model for the next 12 months forecasting. This study has provided useful information for the development of dengue predictions and future warning systems.

Continuous Estimation of the Key Components Content in the Isomerization Process Products

Soft sensors for estimating a fraction of key components in the products of a Low-temperature isomerization process equipped with a deisohexanizer distillation column are developed. Real plant data from the refinery distributed control system (DCS) are used. A considerable attention is paid to data selection, selection of key input variables, data processing and analysis.Dynamic soft sensor models for estimating the fraction of 2,2-Dimethylbutane, 2,3-Dimethylbutane, 2-Methylpentane and 3-Methylpentane in the products of the process are developed based on linear and nonlinear regression techniques. The development of a linear dynamic Finite Impulse Response (FIR), Autoregressive with Exogenous Inputs (ARX), Output Error (OE), as well as Nonlinear Dynamic Autoregressive with Exogenous Inputs (NARX) and Hammerstein-Wiener (HW) models are presented. Developed models were evaluated by validation techniques including Root Mean Square Error (RMSE), Absolute Error (AE), Final Prediction Error (FPE) and FIT coefficients.The results show that the developed soft sensors can reliably estimate the content of key components and thus replace process analysers in the case of failure. This will contribute to the operation stability of the column, the rise in product quality, the reduction in energy consumption as well as the improvement of whole isomerization process. Also, the developed soft sensors can be applied in the Advanced Process Control scheme of the deisohexanizer column.

Application of Wavelet Neural Network in Forward Kinematics Solution of 6-RSU Co-axial Parallel Mechanism Based on Final Prediction Error

Application of artificial neural network (ANN) in forward kinematic solution (FKS) of a novel co-axial parallel mechanism with six degrees of freedom (6-DOF) is addressed in Current work. The mechanism is known as six revolute-spherical-universal (RSU) and constructed by 6-RSU co-axial kinematic chains in parallel form. First, applying geometrical analysis and vectorial principles the kinematic model is extracted and inverse kinematics solution is done. Due to highly nonlinear characteristic of the model, forward kinematic solution for 6-RSU is so complicated. Therefore, ANN based on wavelet analysis, as a powerful solution, is designed and applied to solve FK problem. The minimum prediction risk principle with using final prediction error (FPE) is applied to find the best and optimum topology of our proposed neural network (WNN) in this paper. Furthermore, proposed wavelet WNN is developed to approximate the specific reference trajectories for manipulated platform of mechanism and the results are obtained. Comparing the extracted results by WNN with closed form solution (CFS) demonstrates the accuracy and efficiency of the proposed WNN.

Modeling of greenhouse agro-ecosystem using optimally designed bootstrapping artificial neural network

The greenhouse environment is a complex multi-scale integrated nonlinear system. This agro-ecosystem is composed of crop and greenhouse climate which are based on the existence of two different timescales. The effect of temperature plays a vital role in the variation of phenotypic data in crop growth. Thus, two different models, one for capturing the climate dynamics inside the greenhouse and other for crop dynamics, are essential. First, the neural network is used to predict the inside environment, given the outside conditions and the operation of the control equipment. The inputs of the network are meteorological parameters, whose measurements are costly and time consuming to acquire. So, instead of measuring all the parameters used in the physical modeling, the most significant relevant input parameters which give same modeling efficiency are identified. To avoid overfitting of the data and to realize the best prediction results with the simplest structure, an enhanced pruning algorithm is implemented for topology optimization of the artificial neural network. The pruning algorithm is discussed and exemplified via simulations. By plotting the training error, test error, and final prediction error (FPE) estimates over the course of pruning the network weights, it is inferred that a network with minimum of 15 weights is reliable to model greenhouse environment dynamics. With the Optimal Brain Surgeon (OBS) algorithm, a reduction of the number of weights from 141 to 76 (46%) in the first step and finally to 15 (89%) was achieved and the percentage prediction error is reduced from 13.13% for the complete network structure to 4.35% for final pruned network. Secondly, in order to study the progress of crop ontogeny, bootstrap resampling-based artificial neural network is developed with limited destructive measurements. The notion of prediction performance and the efficiency of the bootstrapped crop phenotypic neural network model are evaluated by root mean square error (RMSE), mean square error (MSE) and Nash and Sutcliffe efficiency (NSE) criteria. The net assimilation rate which determines the growth rate of the plant inside the greenhouse environment is calculated. The resulting model can be used for growth assessment, understanding crop physiology and yield prediction.

Frequency, Damping, and Flutter Prediction from Aircraft Flight Data Using Autoregressive Model

Demonstration of flutter stability over the design envelope and identification of a safe flight envelope is a prerequisite for operational clearance of any new aircraft design. Generally, in all the flight flutter-testing programs, frequency and modal damping ratios are estimated at each flight-test point, and the trend of variation of frequency and damping is established. Frequencies and damping value estimations have to be as accurate as possible to define the aircraft flutter margin at each test point. In this study, stability parameters are estimated directly from the flight flutter-test time response data using an autoregressive (AR) model, which in turn is used to estimate the frequency and damping. In this paper, the focus is on determining an optimized AR model to ensure the accuracy of the model so that the estimation of stability parameters as well as frequency and damping parameters will be more accurate. Toward that, model order estimation techniques such as Akaike’s information criteria and final prediction error were used to predict the model order efficiently. Studies have been presented for different data lengths to prove the capability of this method to produce an accurate spectral estimate even with short data records. This will enable a quick evaluation of spectral estimate and flutter stability parameter using the same AR model, facilitating a quick flight envelope expansion.

Compositional time series analysis for Air Pollution Index data

The increasing importance of understanding the structure of Air Pollution Index (API) makes it necessary to come out with a compositional of API based on its pollutants. This will be more comprehensible for the public and easier to cooperate with authorities in reducing the causes of air pollution. Since five pollutants contribute in determining the API values, API can be shown as a compositional data. This study is conducted based on the data of API and its pollutants collected from Klang city in Malaysia for the period of January 2005 to December 2014. The proportion of each pollutant in API is considered as a component with five components in a compositional API. The existence of zero components in some pollutants, that have no effect on API, is a serious problem that prevents the application of log-ratio transformation. Thus, the approach of amalgamation has been used to combine the components with zero in order to reduce the number of zeros. Also, a multiplicative replacement has been utilized to eliminate the zero components and replace them with a small value that maintains the ratios of nonzero components. Transforming the compositional data to log-ratio coordinates has been done using the additive log ratio transformation, and the transformed series is then modeled by using a VAR model. Four criteria are used to determine the number of lags p of VAR(p) and these are: the Akaike Information, the Schwartz, the Hannan–Quinn and the Final Prediction Error criteria. Based on the results, A VAR (1) model with no constants or trend is considered as the best fitted model and it is used to forecast 12 months ahead. In addition, API values are mainly determined by PM10 that has a proportion close to one most of the time during study period. Therefore, authorities and researchers need to study the sources of PM10 and provide the public with useful information and alternatives in term of reducing the air pollution.

Identification of nonstationary multivariate autoregressive processes – Comparison of competitive and collaborative strategies for joint selection of estimation bandwidth and model order

The problem of identification of multivariate autoregressive processes (systems or signals) with unknown and possibly time-varying model order and time-varying rate of parameter variation is considered and solved using parallel estimation approach. Under this approach, several local estimation algorithms, with different order and bandwidth settings, are run simultaneously and compared based on their predictive performance. First, the competitive decision schemes are considered. It is shown that the best parameter tracking results can be obtained when the order is selected based on minimization of the appropriately modified Akaike's final prediction error statistic, and the bandwidth is chosen using the localized version of the Rissanen's predictive least squares statistic. Next, it is shown that estimation results can be further improved if a collaborative decision is made by means of applying the Bayesian model averaging technique.

NARX-based BPSO modelling for time-varying steam temperature of steam distillation pilot plant

This paper focuses on a nonlinear modelling for a time-varying process of steam temperature by employing a polynomial Nonlinear Auto-Regressive with Exogenous Input (NARX) structure based on Binary Particle Swarm Optimization (BPSO) algorithm. The system identification time-varying steam temperature data was collected from Steam Distillation Pilot Plant. Three models’ criterion were implemented; Akaike Information Criterion, Model Descriptor Length (MDL) and Final Prediction Error (FPE) for optimization process of NARX-based BPSO modelling. The results demonstrated that the FPE criterion model was presented a slightly better model with lowest CRV from the testing set, small fitness value and a minimum number of parameter in the output model. The accuracy was evaluated by the high R-squared, small MSE value and passed all the correlation and histogram tests.

New results on estimation bandwidth adaptation

The problem of identification of a nonstationary autoregressive signal using non-causal estimation schemes is considered. Noncausal estimators can be used in applications that are not time-critical, i.e., do not require real-time processing. A new adaptive estimation bandwidth selection rule based on evaluation of pseudoprediction errors is proposed, allowing one to adjust tracking characteristics of noncausal estimators to unknown and/or time-varying degree of signal nonstationary. The new rule is compared with the previously proposed one, based on the generalized Akaike’s final prediction error criterion.

Hammerstein Model Based RLS Algorithm for Modeling the Intelligent Pneumatic Actuator (IPA) System

An Intelligent Pneumatic Actuator (IPA) system is considered highly nonlinear and subject to nonlinearities which make the precise position control of this actuator is difficult to achieve. Thus, it is appropriate to model the system using nonlinear approach because the linear model sometimes not sufficient enough to represent the nonlinearity of the system in the real process. This study presents a new modeling of an IPA system using Hammerstein model based Recursive Least Square (RLS) algorithm. The Hammerstein model is one of the blocks structured nonlinear models often used to model a nonlinear system and it consists of a static nonlinear block followed by a linear block of dynamic element. In this study, the static nonlinear block was represented by a deadzone of the pneumatic valve, while the linear block was represented by a dynamic element of IPA system. A RLS has been employed as the main algorithm in order to estimate the parameters of the Hammerstein model. The validity of the proposed model has been verified by conducting a real-time experiment. All of the criteria as outlined in the system identification’s procedures were successfully complied by the proposed Hammerstein model as it managed to provide a stable system, higher best fit, lower loss function and lower final prediction error than a linear model developed before. The performance of the proposed Hammerstein model in controlling the IPA’s positioning system is also considered good. Thus, this new developed Hammerstein model is sufficient enough to represents the IPA system utilized in this study.

Forecasting on first generation bioethanol production: A comparison of selected linear and non-linear models

Sustainable bioethanol production depends on the continuity of feedstock supply. Thus, an appropriate tool for feedstock supply forecasting is necessary for bioethanol production. This study was aimed at using forecasting models to predict feedstock supply and then estimating how much bioethanol could be produced from the forecasted bioethanol feedstocks as a major investigation in Turkey. It focused on running the linear model as Auto-Regressive (AR) and non-linear models as Auto-Regressive eXogeneous (ARX) and Auto-Regressive Moving Average eXogeneous (ARMAX) to forecast annual potential of wheat, corn, barley, and sugar beet which could be used as feedstock to produce first generation bioethanol. First, model order determination and modeling of feedstock production were studied for long prediction horizons. Model orders were estimated with major model order selection criteria: Akaike Information Criterion (AIC) and Final Prediction Error in the AR model. The same model orders were also used for the ARX model to compare, whereas model orders were determined based on the performance of the ARMAX model. Second, model performances were tested using Root Mean Square, R2, Chi-Square (χ2), and AIC for optimum model orders of each series. Finally, feedstock forecasts were determined to be quantitatively consistent for each model and with legal authority predictions. There were negligible small differences ranging from 0.8% to 2%. It is concluded that barley and wheat supplies have significant potential to produce bioethanol except for their primary use in food, seed, and feed consumption. However, sugar beet and corn are mainly used in Turkey.

Model Order Selection in Errors-in-Variables System Identification

This work studies the problem of model order selection in errors-in-variables (EIV) system identification. Two criteria, the final correlated prediction error (FCPE) criterion and the final correlated output error (FCOE) criterion are developed for estimating the order of EIV systems. The criteria are extensions of the final prediction error (FPE) criterion and the final output error (FOE) criterion. To eliminate the influence of the input noise in FPE criterion and FOE criterion, the idea of the new criteria is to correlate the prediction error and the output error with the output signal respectively. Simulations are used to illustrate the performance of the criteria.

Recursive System Identification and Simulation of Model Predictive Control Based on Experimental Data to Control the Cathode Side Parameters of the Hybrid Fuel Cell/Gas Turbine

A model predictive control (MPC) strategy has been suggested and simulated with the empirical dynamic data collected on the hybrid performance (HyPer) project facility installed at the National Energy Technology Laboratory (NETL), U.S. Department of Energy, in Morgantown, WV. The excursion dynamic data collected between the setup changes of the actuators on the cathode side of the HyPer facility were processed offline to determine the feasibility of applying an adaptive model predictive control strategy. Bypass valves along with electric load (EL) of the system were manipulated, and variables such as turbine speed, mass flow, temperature, pressure of the cathode side, among others were recorded for analysis. The three main phases of the MPC, identification of the models, control design, and control tuning have been described. Two identification structures, autoregressive exogenous (ARX) and a state-space model, were used to fit the measured data to dynamic models of the facility. The system identification ARX model required around 0.12 s of computer time. The state-space identification algorithm spent around 0.65 s, which was relatively high considering that the sample time of the sensors was 0.4 s. Visual inspection of the tracking accuracy showed that the ARX approach was approximately as accurate as the state-space structure in its ability to reproduce measured data. However, by comparing the loss function and the final prediction error (FPE) parameters, the state-space approach gives better results. For the ARX/state-space models, the MPC was robust in tracking setpoint variations. The MPC strategy described here offers potential to be the way to control the HyPer facility. One of the strengths of MPC is that it can allow the designer to impose strict limits on inputs and outputs in order to keep the system within known safe bounds. Constraints are highly present in the HyPer facility. The constraint airflow valves and the electric load were used in the simulation to control the constraint turbine speed and the cathode airflow (CAF). The MPC also displayed good disturbance rejection on the output variables when the fuel flow was set to simulate fuel cell (FC) heat effluent disturbances. Different off-design scenarios of operation were tested to confirm the estimated implementation behavior of the plant-controller dynamics. One drawback in MPC implementation is the computational time consuming between calculations and will be considered for future studies.