Enriched Imperialist Competitive Algorithm for system identification of magneto-rheological dampers

doi:10.1016/j.ymssp.2015.03.020

Mechanical Systems and Signal Processing

Volumes 62–63, October 2015, Pages 506-516

https://doi.org/10.1016/j.ymssp.2015.03.020 Get rights and content

Highlights

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Enriched Imperialist Competitive Algorithm is introduced to improve the results of non-linear system identification problems.
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The Bouc–Wen model׳s parameters for a MR damper are optimized using EICA algorithm.
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The obtained results demonstrate the high adaptability of EICA to suitably get to the bottom of such non-linear and hysteretic problems.

Abstract

In the current research, the imperialist competitive algorithm is dramatically enhanced and a new optimization method dubbed as Enriched Imperialist Competitive Algorithm (EICA) is effectively introduced to deal with high non-linear optimization problems. To conduct a close examination of its functionality and efficacy, the proposed metaheuristic optimization approach is actively employed to sort out the parameter identification of two different types of hysteretic Bouc–Wen models which are simulating the non-linear behavior of MR dampers. Two types of experimental data are used for the optimization problems to minutely examine the robustness of the proposed EICA. The obtained results self-evidently demonstrate the high adaptability of EICA to suitably get to the bottom of such non-linear and hysteretic problems.

Introduction

As the knowledge in a certain physical problem expands, it is tried to find and include more determining factors to achieve a more accurate simulation of empirical observation. Therefore, the simplified mathematical models are increasingly replaced by the complex models which are accompanied by high-dimensional and non-differential mathematical problems. Conventional mathematical programming methods (e.g. linear programming, homogeneous linear programming, integer programming, dynamic programming, and even non-linear programming) fail to correctly address the parameter identification of systems with high inherent non-linearity and a big number of parameters. Metaheuristic optimization methods have been alternatively utilized to desirably fit the intricate factual behavior of various physical systems to their corresponding high non-linear mathematical models. However, high non-differential characteristics, discrete experimental data and difficulty of estimating a reasonable starting point for parameters׳ search cumulatively make the “system identification” problems to remain a challenging task.

The Bouc–Wen model is a hysteretic non-linear mechanical model in which system׳s response is related to the system׳s input through a first order non-linear differential equation containing a number of unknown parameters. By adjusting these parameters to their optimal values, it is feasible to predict the factual behavior of one hysteretic physical system under any arbitrary input excitations. Charalampakis et al. [1], [2] successfully used a hybrid Evolutionary Algorithm (EA) and Particle Swarm Optimization (PSO) approaches to find the optimal set of Bouc–Wen model parameters for producing the experimentally obtained hysteretic behavior of a steel cantilever beam. Meiying and Xiaodong [3] examined and validated the effectiveness of the PSO estimating parameter characteristics of Bouc–Wen model for experimental data. Kwok et al. [4], [5] applied the Genetic Algorithm (GA) to identify the Bouc–Wen relations modeling hysteretic non-linear behavior of MR dampers. Liu et al. [6] and Talatahari et al. [7] also utilized the Simulated Annealing algorithm (SA) and the Charged System Search (CSS) [8], [9], [10] respectively to optimally find the Bouc–Wen model parameters of MR dampers. Also, Talatahari et al. proposed a hybrid algorithm for solving this problem in [11].

The purpose of the current paper is to effectively improve the so-called Imperialist Competitive Algorithm (ICA) [12], [13], [14], [15] and submit a novel optimization method called as Enriched Imperialist Algorithm (EICA); which could be successfully used for high non-linear optimization problems. Herein, to provide a merit investigation on the efficacy of the proposed approach dealing with high non-linear problems, it is employed to find the optimal parameters of the various types of hysteretic Bouc–Wen models predicting extreme non-linear demeanor of MR fluid dampers. MR dampers are a kind of semi-active energy-dissipating devices that provide controllable damping forces by reforming the magnitude of the applied magnetic field (input voltage). These dampers are actively engaged to mitigate the vibrational responses of civil structures [16], [17], [18], [19] and mechanical systems [20], [21], [22], [23], [24], [25].

Section snippets

Problem formulation

In order to obtain the optimal values of the parameters, a proper objective function shall be determined and engaged by the optimization algorithm. The normalized mean square error (MSE) of the predicted response time history $\hat{f} (t_{i} | p)$ (for any obtained parameters׳ vector p) in comparison with the experimentally obtained response history $f (t_{i})$ at each time step t_i is usually considered as the objective function to be minimized. The discrete–time objective function can be expressed as $O F (p) = \sum_{i = 1}^{N} (f$

A concise overview of original Imperialist Competitive Algorithm

The ICA simulates the social political process of imperialism and imperialistic competition. The agents of this algorithm are called “countries”. There are two types of countries; some of the best countries (in optimization terminology, countries with lower cost) are selected to be the “imperialist” states and the remaining countries form the “colonies” of these imperialists. All the colonies of initial countries are divided among the imperialists based on their “power”. The power of each

Mechanical Bouc–Wen models for MR dampers

Magneto-rheological (MR) dampers are a kind of semi-active control devices which are used to intelligently mitigate the vibrational response of mechanical systems due to external excitations. For the first time, Spencer et al. [26] presented the force of MR dampers through applying a Bouc–Wen model. The standard Bouc–Wen model and a modified one were shown to be capable of reproducing the factual non-linear hysteretic behavior of MR dampers. Elaboration on the role of different parameters of

Numerical study

By adjusting twelve parameters of standard Bouc–Wen model ( $α_{a}$ , $α_{b}$ , $c_{0 a}$ , $c_{0 b}$ , $k_{0 a}$ , $k_{0 b}$ , $x_{0}$ , $γ$ , $β$ , $A$ , $n$ , $η$ ) or fourteen parameters of modified model ( $α_{a}$ , $α_{b}$ , $c_{0 a}$ , $c_{0 b}$ , $c_{1 a}$ , $c_{1 b}$ , $k_{0}$ , $k_{1}$ , $x_{0}$ , $γ$ , $β$ , $A$ , $n$ , $η$ ) to their true optimal values, it is possible to predict the response of a MR damper to any random inputs (displacement and applied voltage) before and after the yield areas. This will be gained through solving an optimization problem with an objective of fitting model׳s response to the

Summary and conclusion

An efficient identification method for differential highly non-linear hysteretic Bouc–Wen models of MR fluid dampers is introduced by the Enriched Imperialist Competitive Algorithm (EICA) as the main contribution of the paper. The EICA simulates the social political process of imperialism and imperialistic competition. The agents or countries are divided into imperialist and colonies. All the colonies of initial countries are divided among the imperialists based on their power. After forming

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Citation Excerpt :
There are different meta-heuristic approaches to find the optimal set of Bouc-Wen model parameters for the experimental data [8,9,38]. Also, different meta-heuristic optimization algorithms were utilized to optimally find the Bouc–Wen model parameters of magneto-rheological (MR) dampers [35,36,50,52]. Others used a hybrid algorithm for the optimal design of MR damper parameters [3].
In this paper, a new hybrid algorithm based on charged system search (CSS) and colliding bodies optimization (CBO) is proposed to identify the parameters of a highly nonlinear semi-active magneto-rheological damper. As particles have limited effect on each other in CBO, CSS is used to enhance the search space which increases the correlation of particles. To investigate the robustness of the proposed new hybrid algorithm, first, the benchmark mathematical functions are used. Then, a modified Bouc-Wen model of MR damper is considered to find its parameters, based on numerically generated experimental data of MR damper. Also, by exploiting the sensitivity analysis and using the importance vector, the low importance parameters in the Bouc-Wen model are eliminated which makes the MR damper model simpler. Results demonstrate that the new proposed hybrid algorithm (H-CBO-CSS) is greatly capable to tackle highly nonlinear problems. Based on the results of the α importance vector, a simplified model is proposed and its parameters are identified using the presented H-CBO-CSS algorithm. The simplified proposed model also has a high capability of estimating damper responses.
Optimizing the sum of maximum earliness and tardiness of the job shop scheduling problem
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Citation Excerpt :
Huang and Süer (2015) proposed a dispatching rule based genetic algorithm with fuzzy satisfaction levels for solving the multi-objective manufacturing scheduling problem where the objectives were makespan, average flow time, maximal tardiness and total tardiness. ICA is a global search algorithm that has been successfully employed in numerous applications (Ali, 2015; Duan & Huang, 2014; Goldansaz, Jolai, & Anaraki, 2013; Maroufmashat, Sayedin, & Khavas, 2014; Mousavi, Tavakkoli-Moghaddam, Vahdani, Hashemi, & Sanjari, 2013; Mohammadi-ivatloo, Rabiee, Soroudi, & Ehsan, 2012; Naderi & Yazdani, 2014; Niknam, Fard, Pourjafarian, & Rousta, 2011; Taghavifar, Mardani, & Taghavifar, 2013; Talatahari & Rahbari, 2015). The main idea behind ICA is to mimic the imperialistic competition process, where powerful countries compete for colonies.
The sum of the maximum earliness and tardiness criteria is a new objective function for the job shop scheduling problem introduced in this work. A mixed integer linear programming (MIP) formulation of the job shop scheduling problem with the new objective function is developed. We design a set of experiments where we validate the MIP model on different problem sizes.
This is one of the most difficult problems in combinatorial optimization, with even modest sized instances being computationally intractable. Getting inspiration from a number of advances in solving this notoriously difficult problem, we develop a new approximate optimization approach, which is based on the imperialist competitive algorithm hybridized with an efficient neighborhood search. The effectiveness of the proposed approach is demonstrated through an experimental evaluation.
EXPLICA: An Explorative Imperialist Competitive Algorithm based on the notion of Explorers with an expansive retention policy
2017, Applied Soft Computing Journal
Citation Excerpt :
Furthermore, since there are several improvements to the original ICA, it is interesting to compare the performance of EXPLICA with other improvements of ICA. Therefore, in this experiment, a modified ICA, Enriched ICA, is also considered [43,42] and its performance is compared. For the sake of brevity, and also because according to Eq. (3.1), with greater dimensions, more computational efforts are allocated to solving the optimization problems, only results of the tests for dimensions D = 60, 90 are reported.
Meta-heuristic algorithms are of considerable importance in solving optimization problems. This importance is more highlighted when the problems to be optimized are too complicated to achieve a solution using conventional methods or, the traditional methods are somehow not applicable for solving them. Imperial Competitive Algorithm has been proved to be an efficient and effective meta-heuristic optimization algorithm and it has been successfully applied in many scientific and engineering problems. By introducing the concept of explorers and retention policy, the original algorithm is enhanced with a dynamic population mechanism in this paper and hence, the performance of the Imperial Competitive Algorithm is improved. Performance of the proposed modification is tested with experiments of optimizing real-values functions and results are compared with results obtained with the original Imperialistic Competitive Algorithm, Genetic Algorithm, Particle Swarm Optimization and Simulated Annealing. Also, the applicability of the proposed improvement is verified by optimizing a ship propeller design problem.
An improved PSO algorithm for parameter identification of nonlinear dynamic hysteretic models
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Citation Excerpt :
In their research, the Nelder-Mead simplex method was used to refine the initial results calculated by the genetic algorithm. Talatahari and Rahbari [4] proposed the enriched imperialist competitive algorithm for the parameter identification of magneto-rheological dampers. As a random searching algorithm, the Particle Swarm Optimization (PSO) algorithm [5] iteratively updates the positions of particles which have the ability to remember and share the information to obtain the optimal solution.
The nonlinear dynamic hysteretic models used in nonlinear dynamic analysis contain generally lots of model parameters which need to be identified accurately and effectively. The accuracy and effectiveness of identification depend generally on the complexity of model, number of model parameters and proximity of initial values of the parameters. The particle swarm optimization (PSO) algorithm has the random searching ability and has been widely applied to the parameter identification in the nonlinear dynamic hysteretic models. However, the PSO algorithm may get trapped in the local optimum and appear the premature convergence not to obtain the real optimum results. In this paper, an improved PSO algorithm for identifying parameters of nonlinear dynamic hysteretic models has been presented by defining a fitness function for hysteretic model. The improved PSO algorithm can enhance the global searching ability and avoid to appear the premature convergence of the conventional PSO algorithm, and has been applied to identify the parameters of two nonlinear dynamic hysteretic models which are the Leishman-Beddoes (LB) dynamic stall model of rotor blade and the anelastic displacement fields (ADF) model of elastomeric damper which can be used as the lead-lag damper in rotor. The accuracy and effectiveness of the improved PSO algorithm for identifying parameters of the LB model and the ADF model are validated by comparing the identified results with test results. The investigations have indicated that in order to reduce the influence of randomness caused by using the PSO algorithm on the accuracy of identified parameters, it is an effective method to increase the number of repeated identifications.
Comparing optimization algorithms for parameter identification of sigmoid model for MR damper
2024, Journal of the Brazilian Society of Mechanical Sciences and Engineering
Comparing optimization algorithms for Parameter Identification of Sigmoid Model for MR damper
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View full text

Enriched Imperialist Competitive Algorithm for system identification of magneto-rheological dampers

Highlights

Abstract

Introduction

Section snippets

Problem formulation

A concise overview of original Imperialist Competitive Algorithm

Mechanical Bouc–Wen models for MR dampers

Numerical study

Summary and conclusion

J. Sound Vib.

Comput. Struct.

ISA Trans.

Comput. Struct.

Mechatronics

Parameter estimation of the Bouc–Wen hysteresis model using particle swarm optimization

Smart Mater. Struct.

Parameter identification of Bouc–Wen model for mr fluid dampers using adaptive charged system search optimization

Mech. Sci. Technol.

A novel heuristic optimization method: charged system search