Parametric identification of seismic isolators using differential evolution and particle swarm optimization

doi:10.1016/j.asoc.2014.04.039

Applied Soft Computing

Volume 22, September 2014, Pages 458-464

https://doi.org/10.1016/j.asoc.2014.04.039 Get rights and content

Highlights

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This paper is concerned with the parametric identification of seismic isolators.
•
The Bouc–Wen model is considered to simulate the hysteretic response.
•
Parametric identification is performed using two soft computing techniques.
•
Experimental data are carried out from standardized qualification tests.
•
Good agreement is found between experimental data and numerical simulations.

Abstract

The objective of a base isolation system is to decouple the building from the damaging components of the earthquake by placing isolators between the superstructure and the foundation. The correct identification of these devices is, therefore, a critical step towards reliable simulations of base-isolated systems subjected to dynamic ground motion. In this perspective, the parametric identification of seismic isolators from experimental dynamic tests is here addressed. In doing so, the focus is on identifying Bouc–Wen model parameters by means of particle swarm optimization and differential evolution. This paper is especially concerned with the assessment of these non-classical parametric identification techniques using a standardized experimental protocol to set out the dynamic loading conditions. A critical review of the obtained outputs demonstrates that particle swarm optimization and differential evolution can be effectively exploited for the parametric identification of seismic isolators.

Graphical abstract

Introduction

The use of base-isolators for protecting buildings, bridges, liquid storage tanks, oil pipelines, and nuclear reactor plants against the damaging effects of seismic loadings has become very frequent in recent decades [1], [2]. The advantage of base isolation systems lies in avoiding that the damaging effects of the earthquakes reach the structures by placing particular devices (isolators) between the protected system and the foundation. In most of the seismic isolators, thin reinforcing steel plates are alternated with thick rubber pads. Conventional isolators are basically produced in two phases: first, the compounded rubber sheets with the interleaved steel plates are put into a mold, and heating under pressure for several hours (the so-called vulcanization) is then performed to complete the manufacturing process. The performance of a seismic isolator depends on many factors, such as the rubber typology, the compound, the thickness and the process of vulcanization of the pads. So far, the Bouc–Wen hysteretic model is considered the most appropriate to simulate the nonlinear behavior of seismic isolators. However, because of the lack of settled relationships between mechanical model and properties of the isolator (i.e., the degree of vulcanization or the precise compound used to build the device), the correctness of the structural simulations requires a reliable identification of the model parameters from experimental tests.

Among the available numerical techniques, non-classical approaches based on soft computing methods are attracting growing interests in system identification and damage detection, see for instance Refs. [3], [4]. Within this framework, the parametric identification problem for multi-degree-of-freedom structural linear systems was resolved using genetic algorithm (GA) [5], Big Bang–Big Crunch optimization [6], particle swarm optimization (PSO) and differential evolution (DE) [7]. Soft computing-inspired techniques are also exploited for the parametric identification of nonlinear dynamic systems. An overview about the most recent applications in this field [8] revealed that GAs are frequently employed in the parametric identification of hysteresis models, such as the Bouc–Wen model, the Jiles–Atherton model, and the Preisach model. On the other hand, PSO and DE were considered in the parametric identification of hysteresis models [9], [10], viscous damping [11], [12], and Van der Pol-Duffing oscillators [13].

The use of non-classical methods for the parametric identification of Bouc–Wen-type models has been continuously gaining increased attention in literature. For instance, a multi-species GA was proposed in Ref. [14] to identify Bouc–Wen models from noisy data. A Bouc–Wen model was identified by means of DE in Ref. [15], where the authors presented some results for experimental data obtained from a nuclear power plant. Kwok and co-authors [16] used a GA to identify a non-symmetrical Bouc–Wen model proposed to represent the hysteretic behavior of magnetorheological fluid dampers. A memetic GA and a PSO algorithm were adopted in Refs. [17], [18], respectively, to reproduce the cyclic response of a bolted–welded steel connection through a Bouc–Wen model. A generalized Bouc–Wen model was considered in Ref. [19] for predicting the cyclic response of a T-connection consisting of two wood members joined by plywood gusset plates, and the parametric identification problem was solved by using a DE algorithm. Recently, Worden and Manson [20] investigated the effectiveness of a self-adaptive DE algorithm for the parametric identification of the Bouc–Wen model using simulated noisy data.

In this paper, the focus is on identifying Bouc–Wen parameters for seismic isolation devices by means of non-classical methods, a problem which has received very few attention. A recent article by Sireteanu and co-authors [21] on this topic addressed the GA-based parametric identification of an extended Bouc–Wen model for elastomeric bearings. Differently from that paper, the parametric identification of seismic isolators is here performed for the first time by means of PSO and DE. Such techniques have a simple structure and require few control parameters, whose optimal values lie within a rather small interval. These characteristics, together with the numerical robustness, are especially important for industrial applications. The feasibility of these soft computing techniques is critically reviewed with reference to experimental data. In this sense, other significant contributions are concerned with the experimental protocol and the completeness of the final results. The examined device was subjected to loading conditions imposed by standardized qualification tests for seismic isolators (the current Italian building code [22] is taken into account in this study). This is to ensure the objectivity of the results with respect to the current state-of-the-practice about the experimental qualification of seismic isolators. In doing so, this study also benefits of a larger experimental database than the considered one in previous researches [21]. Moreover, although identification methods for nonlinear systems are usually examined by considering the displacement-force curves only (as in Ref. [21]), this paper also evaluates the quality of the whole procedure with reference to the velocity-force curves. This complete analysis turns out to be very important for assessing the real effectiveness of such techniques for industrial applications. Final results demonstrate that PSO and DE can be viable tools for the parametric identification of seismic isolators, and that the DE algorithm is significantly better than PSO.

Section snippets

Hysteresis model for seismic isolators

The seismic isolator is modeled as nonlinear single-degree-of-freedom system: $m \ddot{y} (t) + ϕ (t) = g (t),$ where m is the mass, y(t) is the displacement (overdots denote the time-derivative), ϕ(t) is the restoring force and g(t) is the excitation dynamic load. As usual in nonlinear modeling of isolators [23], damping is represented by taking into account the inelastic (hysteretic) response of the isolators whereas viscous damping is not included. So doing, by assuming a Bouc–Wen hysteresis model, the

Particle swarm optimization algorithm

The ith particle (with i = 1, …, m) at the kth iteration has two attributes, a velocity ${{}^{k}v}_{i} = {\begin{matrix} {{}^{k}v}_{i 1} & \dots & {{}^{k}v}_{ij} & \dots & {{}^{k}v}_{in} \end{matrix}} \in ℝ^{1 \times n}$ and a position ${{}^{k}x}_{i} = {\begin{matrix} {{}^{k}x}_{i 1} & \dots & {{}^{k}x}_{ij} & \dots {{}^{k}x}_{in} \end{matrix}} \in ℝ^{1 \times n}$ . In order to protect the cohesion of the swarm, the absolute value of the velocity ${{}^{k}v}_{ij}$ is assumed to be less than a maximum velocity $v_{j}^{\max}$ , with $v^{\max} = {\begin{matrix} v_{1}^{\max} & \dots & v_{j}^{\max} & \dots & v_{n}^{\max} \end{matrix}}$ . It is assumed v^max = γ(x^u − x^l)/Δτ, with γ = 0.50 [13]. The internal time variable Δτ = 1 is introduced to provide a physically consistent formalism. The initial set of candidate

Experimental setup

The testing machine (see Fig. 1) basically consists of a high resistance steel frame to withstand horizontal loads (in both directions) up to 2200 kN and vertical loads of compression up to 10,000 kN. The maximum allowable horizontal displacement is ±260 mm. A LABVIEW based platform allows for the real-time system control, data acquisition and visualization.

Experimental data for parametric identification are carried out from standardized experimental tests. In detail, this paper considers the

Conclusions

This paper addressed the parametric identification of seismic isolators by means of non-classical (soft computing based) methods. A Bouc–Wen model has been considered in order to simulate the hysteretic response of the seismic isolators, and the parametric identification is posed as minimization problem. Subsequently, model parameters are identified solving this optimization problem by means of particle swarm optimization algorithm and differential evolution algorithm. These identification

Acknowledgements

The authors wish to thank Eng. Ciro Caramia and Dr. Jennifer Avakian (SISMALAB srl) for having performed the experiments.

The first author has contributed to this work while visiting the Loughborough University (UK). He would like to thank the warm hospitality received, in particular, from Alessandro Palmeri.

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Parametric identification of seismic isolators using differential evolution and particle swarm optimization

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Hysteresis model for seismic isolators

Particle swarm optimization algorithm

Experimental setup

Conclusions

Acknowledgements

Appl. Soft Comput.

Appl. Soft Comput.

Mech. Syst. Signal Process.

Comput. Struct.

Mech. Syst. Signal Process.

Expert Syst. Appl.

Mech. Syst. Signal Process.

J. Sound Vib.

ISA Trans.

J. Sound Vib.

Comput. Struct.