Enriched Imperialist Competitive Algorithm for system identification of magneto-rheological dampers
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 (for any obtained parameters׳ vector p) in comparison with the experimentally obtained response history at each time step ti is usually considered as the objective function to be minimized. The discrete–time objective function can be expressed as
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 (, , , , , , , , , , , ) or fourteen parameters of modified model (, , , , , , , , , , , , , ) 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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Reliability-based simplification of Bouc-Wen model and parameter identification using a new hybrid algorithm
2020, StructuresCitation 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].
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2017, Computers and Industrial EngineeringCitation 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.
EXPLICA: An Explorative Imperialist Competitive Algorithm based on the notion of Explorers with an expansive retention policy
2017, Applied Soft Computing JournalCitation 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.
An improved PSO algorithm for parameter identification of nonlinear dynamic hysteretic models
2017, Journal of Sound and VibrationCitation 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.
Comparing optimization algorithms for parameter identification of sigmoid model for MR damper
2024, Journal of the Brazilian Society of Mechanical Sciences and Engineering