A two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization

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Abstract

A two-stage method is proposed here to properly identify the site and extent of multiple damage cases in structural systems. In the first stage, a modal strain energy based index (MSEBI) is presented to precisely locate the eventual damage of a structure. The modal strain energy is calculated using the modal analysis information extracted from a finite element modeling. In the second stage, the extent of actual damage is determined via a particle swarm optimization (PSO) using the first stage results. Two illustrative test examples are considered to assess the performance of the proposed method. Numerical results indicate that the combination of MSEBI and PSO can provide a reliable tool to accurately identify the multiple structural damage.

Highlights

► A two-stage method is proposed to properly identify the structural damage. ► Damage can be accurately located using a modal strain energy based index (MSEBI). ► The extent of damage is determined via a particle swarm optimization (PSO). ► The combination of MSEBI and PSO is an efficient tool for identifying the damage.

Introduction

Health monitoring and damage identification is an imperative issue in structural engineering. Using this concept the local damage of a structure can be detected and after rehabilitating the damage, the functional age of the structure will increase. Mathematically, the problem of structural damage identification is a highly non-linear problem and special methods must be employed to properly solve it. In recent years, many methods have been introduced to detect the site and extent of damage in the structural systems [1], [2], [3], [4], [5]. One type of the methods employs the optimization algorithms for detecting the multiple structural damage. Many successful applications of damage detection using the genetic algorithm (GA) have been reported in the literature [6], [7], [8], [9]. Although, the use of an optimization algorithm enables us to identify the structural damage, however, they impose much computational effort to the process due to a great numbers of damage variables. In order to reduce the computational cost of the optimization process, some useful techniques can be employed. A useful technique is to reduce the dimension of optimization problem by excluding the healthy elements firstly and then applying the optimization method to the reduced problem for determining the extent of damaged elements [10], [11], [12].

In this study, a two-stage method of determining the location and extent of multiple structural damage is proposed. In the first stage, the damage is located using the concept of modal strain energy (MSE). For this, a modal strain energy based index (MSEBI) is proposed here. In the second stage, the particle swarm optimization (PSO) as a widespread optimization solver is utilized to determine the extent of damaged elements sited in the first stage. Numerical results show the high efficiency of the proposed method for accurately identifying the location and extent of multiple structural damage.

Section snippets

Structural damage detection

Structural damage detection techniques are generally classified into two main categories. They include the dynamic and static identification methods requiring the dynamic and static test data, respectively. Furthermore, the dynamic identification methods have shown their advantages in comparison with the static ones. Among the dynamic data, the modal analysis information of a structure such as the natural frequencies and mode shapes has been widely used for damage detection [1], [4], [11].

Modal strain energy based index

In this study, an efficient index based on the modal strain energy (MSE) is presented to accurately site the flawed elements of a damaged structure. The modal analysis is a tool to determine the natural frequencies and mode shapes of a structure. It has the mathematical form of [14](Kωi2M)φi=0,i=1,,ndfwhere K and M are the stiffness and mass matrices of the structure, respectively; ωi and φi are the ith circular frequency and mode shape vector of the structure, respectively. Also, ndf is the

Particle swarm optimization

In this study a particle swarm optimization (PSO) is employed to determine the damage extent located properly by the MSEBI. The aim is to find a set of reduced damage variables Xr maximizing the MDLAC asFindXrT={xr1,xr2,,xrm}Minimize:w(Xr)=MDLAC(Xr)xriRd,i=1,,mwhere Rd is a given set of discrete values and the damage extent xri(i=1,,m) can take values only from this set. Also, w is an objective function that should be minimized.

The PSO has been inspired by the social behavior of animals

Test examples

In order to show the capabilities of the proposed method for identifying the multiple structural damage, two illustrative test examples are considered. The first example is a 15-element cantilevered beam discussed in detail and the second one is a 31-bar planar truss. In the first example, the measurement noise is ignored whereas the effect of measurement noise on the performance of the method is considered in the second example.

Conclusions

A two-stage method for identifying the location and extent of multiple damage in the structural systems has been proposed. In the first stage, the potentially flawed elements of a damaged structure are located via a modal strain energy based index (MSEBI) presented. The MSEBI is based on the change of modal strain energy (MSE) between the undamaged structure and damaged structure. In the second stage, the reduced damage problem having much fewer damage variables is solved using a particle swarm

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