NARMAX Model Identification Using Multi-Objective Optimization Differential Evolution

Multi-objective optimization differential evolution (MOODE) algorithm has demonstrated to be an effective algorithm for selecting the structure of nonlinear auto-regressive with exogeneous input (NARX) model in dynamic system modeling. This paper presents the expansion of the MOODE algorithm to obtain an adequate and parsimonious nonlinear auto-regressive moving average with exogenous input (NARMAX) model. A simple methodology for developing the MOODE-NARMAX model is proposed. Two objective functions were considered in the algorithm for optimization; minimizing the number of term of a model structure and minimizing the mean square error between actual and predicted outputs. Two simulated systems and two real systems data were considered for testing the effectiveness of the algorithm. Model validity tests were applied to the set of solutions called the Pareto-optimal set that was generated from the MOODE algorithm in order to select an optimal model. The results show that the MOODE-NARMAX algorithm is able to correctly identify the simulated examples and adequately model real data structures

Perturbation parameters tuning of multi-objective optimization differential evolution and its application to dynamic system modeling

This paper presents perturbation parameters for tuning of multi-objective optimization differential evolution and its application to dynamic system modeling. The perturbation of the proposed algorithm was composed of crossover and mutation operators. Initially, a set of parameter values was tuned vigorously by executing multiple runs of algorithm for each proposed parameter variation. A set of values for crossover and mutation rates were proposed in executing the algorithm for model structure selection in dynamic system modeling. The model structure selection was one of the procedures in the system identification technique. Most researchers focused on the problem in selecting the parsimony model as the best represented the dynamic systems. Therefore, this problem needed two objective functions to overcome it, i.e. minimum predictive error and model complexity. One of the main problems in identification of dynamic systems is to select the minimal model from the huge possible models that need to be considered. Hence, the important concepts in selecting good and adequate model used in the proposed algorithm were elaborated, including the implementation of the algorithm for modeling dynamic systems. Besides, the results showed that multi-objective optimization differential evolution performed better with tuned perturbation parameters

Comparison of Evolutionary Computation and Empirical Penman-Monteith Equation for Daily and Monthly Reference Evapotranspiration Estimation in Tropical Region

Evapotranspiration is the combination of evaporation and transpiration processes that give means the process of water loss to the atmosphere. Reference evapotranspiration (ETo) estimation is part of water cycle that importance for planning and management of irrigation purposes and water resource systems. Due to its importance, the accurate modeling of ETo is of vital importance to estimate crop water requirement and its availability. This research presents a system identification and differential evolution approach by using Differential Evolution and System Identification (DESI) and Modified Genetic Algorithm (MGA) approach for modeling daily and monthly ETo in peninsular of Malaysia. The data set comprising air temperature, humidity, wind speed, and solar radiation was utilized for estimating ETo using FAO56 Penman Monteith (PM) equation as the reference. The modeling results were analyzed and compared with the traditional Penman Monteith method. Based on the analyses, the approach used was found that the models of ETo is adequate and understandable, and suited to estimate the dynamics of the evapotranspiration process. The performance of the model is comparable with that of the PM method

Comparison of evolutionary computation and empirical Penman-Monteith equation for daily and monthly reference evapotranspiration estimation in tropical region

Evapotranspiration is the combination of evaporation and transpiration processes that give means the process of water loss to the atmosphere. Reference evapotranspiration (ETo) estimation is part of water cycle that importance for planning and management of irrigation purposes and water resource systems. Due to its importance, the accurate modeling of ETo is of vital importance to estimate crop water requirement and its availability. This research presents a system identification and differential evolution approach by using Differential Evolution and System Identification (DESI) and Modified Genetic Algorithm (MGA) approach for modeling daily and monthly ETo in peninsular of Malaysia. The data set comprising air temperature, humidity, wind speed, and solar radiation was utilized for estimating ETo using FAO56 Penman Monteith (PM) equation as the reference. The modeling results were analyzed and compared with the traditional Penman Monteith method. Based on the analyses, the approach used was found that the models of ETo is adequate and understandable, and suited to estimate the dynamics of the evapotranspiration process. The performance of the model is comparable with that of the PM method

Evapotranspiration prediction using system identification and genetic algorithm

Reference evapotranspiration or ETO is important to provide information in planning and management of water resource system for irrigation purposes. Hence, its accurate estimation is of vital importance to assess water availability and requirements. This study explores the use of system identification approach and modified genetic algorithm (MGA) to model the evapotranspiration process under climatic data. The method is applied in modelling hourly evapotranspiration in central and southern region of Malaysia as a function of solar radiation, temperature, humidity and wind speed. The performance of the model is compared with the traditional Penman-Monteith (PM) method. Results from the study indicate that both the data driven is comparable with that of the PM method. The MGA models are dominated by temperature and solar radiation indicating that these two inputs can represent most of the variance. The results also show that the models are parsimonious and understandable, and are well suited to modelling the dynamics of the evapotranspiration process

Comparison between multi-objective and single-objective optimization for the modeling of dynamic systems

Modeling input–output data representing a dynamic system is a challenging task when multiple objectives are involved. The developed model needs to be parsimonious yet still adequate. To achieve these goals, two objective functions, i.e. optimum structure and minimum predictive error, need to be satisfied. Most works in system identification only consider one objective function, i.e. minimum predictive error, and the model structure is obtained by trial and error. This paper attempts to establish the needs of a multi-objective optimization algorithm by comparing it with a single-objective optimization algorithm. In this study, two different types of optimization algorithms are used to model a discrete-time system. These are an elitist non-dominated sorting genetic algorithm for multi-objective optimization and a modified genetic algorithm for single-objective optimization. Simulated and real systems data are studied for comparison in terms of model predictive accuracy and model complexity. The results show the advantage of the multi-objective optimization algorithm compared with the single-objective optimization algorithm in developing an adequate and parsimonious model for a discrete-time system

Multiobjective Evolutionary Algorithm Approach in Modeling Discrete-Time Multivariable Dynamics Systems

Multiobjective evolutionary algorithms are robust tool in solving many optimization problems. Model structure selection is a procedure in system identification procedures. This procedure counters two contradicting objective functions which are minimizing mean square error and complexity of the selected model. This paper investigates the effectiveness and the performance of multiobjective evolutionary algorithm using elitist nondominated sorting genetic algorithm (NSGA-II) in identifying the model structure for discrete-time multivariable dynamic systems. Two simulated multivariable systems and a real multivariable system, which is a jacketed continuous stirred tank reactor, were used to investigate the effectiveness of NSGA-II. The identified model is validated using one-step-ahead prediction. The results indicate that NSGA-II is able to optimize the model structure of the multivariable systems with good predictive accuracy and adequate model structure

Online optimal tuning of fuzzy PID controller using grey wolf optimizer for quarter car semi-active suspension system

In order to reduce vibration and increase ride comfort, this article utilizes a system of quarter-car suspension integrated with a Fuzzy PID controller. To build and improve the Fuzzy PID controller for the semi-active suspension system used in quarter cars, using a novel meta-heuristic technique known as Grey Wolf Optimizer (GWO). Here the magnetorheological damper (MR) fluid with the Fuzzy PID controller was examined to optimize using the GWO algorithm. With the GWO technique and the integral of time absolute error (IAE) as a fitness function, the three gain parameters of the Fuzzy PID controller – K p , K i , and K d – have been optimally set. The suggested approach has additional advantages for the optimization of functions with three variables, including simplicity in implementation, quick convergence traits, and superior computational capabilities. This work is significant, to the best of the author’s knowledge there is no optimization method using GWO to online tune a Fuzzy PID controller for a semi-active suspension system. The optimal output parameters of the controller can be updated online in real-time by GWO. The performance of the proposed controller was examined by assessing the root mean square (RMS) values and peak-to-peak (PTP) values of body displacement and body acceleration under various road profiles. To ensure that the intelligent controller was of the highest caliber, an online test rig was constructed. Results from simulations and online experiments demonstrated that the Fuzzy GWO PID controller significantly improved ride comfort under a variety of road conditions when compared to the Fuzzy PID controller and passive suspension system