A two-step method for damage identification in moment frame connections using support vector machine and differential evolution algorithm
Graphical abstract
Introduction
Occurrence of damage in structural systems such as buildings, bridges, oil platforms and so on is inevitable in their lifetime. There are many examples of damage in structures that have been led to an overall failure. In order to prevent from spreading the local damage to overall one, it is important to identify and repair damage by inspecting the current status of structures. Damage identification methods are categorized into destructive and non-destructive methods. The destructive methods are not a suitable method for most structures because of their cost and inefficiency, hence, researchers turned to non-destructive methods. One of the most important non-destructive identification methods is based on observing the change in structural responses such as dynamic and static responses. The changes in structures due to damage are shown better by dynamic responses, made the dynamic based methods more popular.
The damage identification in structures should be in some way that the location and severity of damage in structures are accurately determined. Over the last few years, various methods have been proposed to identify damage in structural members, however, damage identification in connections has been less studied. This issue in earthquake-zone areas that a localized damage in connections may be led to an overall failure of structure, increases the importance of damage identification in connections.
In 2001, a research was carried out by Yun et al. for estimating the joint damage of a steel structure from modal data using a neural network technique. The beam-to-column connection in a steel frame structure was modeled by a zero-length rotational spring at the end of the beam element. The severity of joint damage is defined as the reduction of the connection fixity factor. The concept of sub-structural identification was used to assess the localized damage in a large structure. It was found that damage in a joint can be reasonably estimated even for the case where the measured modal vectors were limited to a localized sub-structure and data were severely contaminated with noise [1]. A method for estimating the damage intensities of joints for truss bridge structures using a back-propagation based neural network was presented by Mehrjoo et al. in 2008. In the study, the natural frequencies and mode shapes were used as input parameters to the neural network for damage identification, particularly for the case with incomplete measurements of the mode shapes. A simple truss and a real truss bridge were considered as numerical examples to demonstrate the efficiency of the proposed method. The results showed that, the location and severity of damage in joints of truss bridges can be found with a good precision and the proposed method is attractive for on-line or real-time damage diagnosis of structures in the framework of structural health monitoring [2]. In 2010, local damage identification in beam–column connections using a dense sensor network was carried out by Labuz et al. A prototype beam–column connection was constructed and instrumented by a dense sensor network. Damage was introduced to the system by replacing a portion of the beam element with a smaller section, and thus reduced its stiffness. The results showed that densely clustered sensor network was successfully implemented for local damage identification of both a simulated model as well as an experimental prototype of a steel beam–column connection. Linear regression was used to estimate the influence coefficients from vibration-induced acceleration responses of the structure. By statistically comparing influence coefficients, damage was accurately diagnosed to a 95% confidence bound made the propose method be efficient [3]. In 2013, a two-stage improved radial basis function (IRBF) neural network technique to predict the joint damage of a fifty-member frame structure with semi-rigid connections in both frequency and time domain was proposed by Machavaram and Shankar. The conventional RBF network was used in the first stage of IRBF network and in the second stage reduced search space moving technique was employed for accurate prediction with less than 3% error. The prediction results of the proposed IRBF method were compared with those of conventional RBF method and the CPN–BPN hybrid method in terms of accuracy and computational effort with and without addition of noise to the input patterns in both domains. The results showed that there is a significant improvement in the prediction performance of the novel IRBF method compared to the conventional RBF method and the CPN–BPN hybrid method [4]. In 2014, a method based on a particle swarm optimization (PSO) was introduced by Nanda et al. to identify damage in beam to column connections of framed structures. The joint damage was measured as the ratio of reduction in joint fixity factor at connections. The results indicated that the method has an appropriate accuracy in identifying damage in connections [5]. In 2015, a research was carried out by Ghiasi et al. where 7 artificial intelligence (AI) methods including back-propagation neural networks, least squares support vector machines (LS-SVMs), adaptive neural-fuzzy inference system, radial basis function neural network, large margin nearest neighbor, extreme learning machine (ELM), were used to identify the location and severity of damage in structures. By considering the dynamic behavior of a structure as input variables, seven AI methods are constructed, trained and tested to detect the location and severity of damage in structures. The variation of running time, mean square error, number of training and testing data, and other indices for measuring the accuracy in the prediction were considered to inspect advantages as well as the shortcomings of each algorithm. The results indicated that the ELM and LS-SVM methods demonstrate a better performance in predicting the location and severity of damage than other methods [6]. In 2015, a research was carried out by Satpal et al. which used support vector machine (SVM) to identify damage in aluminum beams. In the work, SVM was explored to find damage locations in aluminum beams using simulation data and experimental data. Displacement values corresponding to the first mode shape of the beam were used to predict the damage locations. Damages are introduced in the form of rectangular notches along the width of the beam at different locations [7]. In 2016, a study was carried out by Ghiasi et al. which used the least square support vector machines (LS-SVM) based on a new combinational kernel function named as thin plate spline Littlewood–Paley wavelet (TPSLPW). During the structural damage identification process, a harmony search algorithm was used to optimize the LS-SVM and TPSLPW parameters. The research indicated the high accuracy of LS-SVM with TPSLPW in detecting damage compared to some methods based on other kernel functions in the same conditions [8]. In 2017, a method using incomplete modal data by Bayesian approach and model reduction technique was proposed by Yin et al. for detecting damage in structural connections. The research presented a practical method for structural bolted-connection damage identification using noisy incomplete modal parameters identified from a limited number of sensors. The efficiency of the proposed methodology was demonstrated by numerical simulations and experimental verifications. In addition, the results showed that the bolt loosening has a substantial influence on the connection stiffness of the bolted joint for the frame-type structure, so more attention needs to be paid in the design and service stages [9].
Most researches reviewed above employed an artificial intelligence method for damage identification. The main drawback of an artificial intelligence based model is that when damage variables increase or data are contaminated by the measurement noise, their efficiency for accurately identifying damage may be decreased. As a result, their solutions need to be improved by another technique such as an optimization method. During the last years, numerous optimization algorithms have been introduced for different applications. Some recently proposed optimization algorithms can be described as below.
In 2017, an improved modified gray wolf optimizer (GWO) algorithm was proposed by Heidari and Pahlavani to solve either global or real-world optimization problems. In order to boost the efficiency of GWO, Lévy flight (LF) and greedy selection strategies were integrated with the modified hunting phases. Experimental results and statistical tests demonstrated that the performance of the modified Lévy-embedded GWO (LGWO) is significantly better than GWO and many optimization algorithms [10]. A new hybrid stochastic training algorithm using the grasshopper optimization algorithm (GOA) for multilayer perceptrons (MLPs) neural networks was proposed by Heidari et al. The proposed GOAMLP model was then applied to five important datasets: breast cancer, Parkinson, diabetes, coronary heart disease, and orthopedic patients and the results were confirmed in comparison with eight recent algorithms. It was proved that the proposed GOAMLP is significantly valuable in improving the classification rate of MLPs. In 2018, a wrapper-feature selection algorithm was proposed based on the binary dragonfly algorithm (BDA) by Mafarja et al. The performance of the dragonfly algorithm was improved using different transfer functions (TFs) to convert the step vector from continuous to a binary space. Eight different TFs that belong to two groups (S-shaped and V-shaped) were employed to investigate their effectiveness on the basic BDA. Results showed that the time-varying S-shaped BDA approach outperforms compared approaches [11]. In 2018, A grasshopper optimization algorithm (GOA) was employed as a search strategy to design a wrapper-based feature selection method by Mafarja et al. An efficient optimizer based on the simultaneous use of the GOA, selection operators, and evolutionary population dynamics (EPD) was proposed in the form of four different strategies to mitigate the immature convergence and stagnation drawbacks of the conventional GOA. The proposed approaches were utilized to tackle 22 benchmark datasets. The comparative results shown the effectiveness of the proposed algorithm for solving different feature selection tasks [12]. In 2019, an intelligent detection system based on genetic algorithm (GA) and random weight network (RWN) was proposed by Faris et al. to deal with email spam identification tasks. An automatic detection ability was also embedded in the proposed system to detect the most relevant features during the identification process. The experimental results confirmed that the proposed system can achieve significant results in terms of accuracy, precision, and recall. Furthermore, the proposed detection system can automatically identify the most relevant features of the spam emails [13]. In 2019, an enhanced whale optimization algorithm (WOA) was proposed with a modified global searching operator by Heidari et al. to mitigate the immature convergence of the WOA and tackle different optimization challenges. The results were compared with different well-known techniques on multi-dimensional classic problems. The experiment tests revealed the superiority of the proposed algorithm compared to standard WOA and several well-established algorithms [14].
The main purpose of this study is to introduce a two-step method for identifying damage in moment frame connections using support vector machine (SVM) and differential evolution algorithm (DEA). In the first step, to determine the possible damage location in connections and reduce damage variables, SVM is used and in the second step, an optimization method named DEA is employed to determine the accurate location and the severity of damage. Numerical results indicate the efficiency of the proposed method. The speed and accuracy of finding damage can be increased by the two-step method when comparing with methods based only on an optimization approach. Moreover, the proposed method is more accurate than an artificial intelligence method.
Section snippets
Damage simulation in moment frame connections
Among the variety of connections, beam-to-column connections in steel structures are generally considered as rigid or pinned and designed. There are various methods for modeling the behavior of connections divided into two main groups: mathematical models and mechanical models that in this paper a mechanical model is used. The mechanical models are known as springy models, based on the simulation of the joint or connection using a zero-length torsional spring at the end of the beam connected to
Support vector machine algorithm
The original SVM algorithm [19] was introduced by Vladimir Vapnik and Alexey Chervonenkis in 1963. The algorithm is one of the supervised learning models generally used for two important issues: classification and regression. In classification issue, SVM is used and in the regression issue employed in this article, a special case of SVM called support vector regression (SVR) is used [19]. In many applications for analyzing a system, at the first step the behavior of the system is modeled based
Damage identification using an optimization method
The purpose of the damage identification using an optimization method is to accurately determine the location and severity of damage. Due to various reasons such as increasing damage variables and the noise effect, the SVM algorithm may achieve some false locations of the damage in addition to exact location. Therefore, an optimization process is used here as the second stage, to modify possible errors. The general form of the optimization problem related to identifying the damage can be
Steps to the research
To do research, at the first an analytical model is provided to simulate the moment frames with semi-rigid connections and then using the model, some structures having damage are randomly generated and natural frequencies of damaged structures are extracted. Then, using a part of the data, SVM is trained, with the difference that the role of input and output data is changed, that is, the natural frequencies are considered as input data and the damage properties are considered as output data. In
Numerical examples
In order to demonstrate the efficiency of the proposed method for identifying damage in moment frame connections, two planar-steel frame structures with 18 elements and 49 elements are investigated. For the mentioned frames, the modulus of elasticity is and the mass density is . The height of the columns in the ground floor is 4.5 m and for other floors is considered 3.5 m. The length of the beams in all floors is 7 m. In these structures, single and double damage cases are
Comparative study
In order to compare the performance of the proposed method with that of an existing method [5] based on optimization using PSO, 30-element frame having 30 nodes is considered as shown in Fig. 30. The cross section of the frame elements are 30 mm width and 6 mm depth. The frame is modeled using aluminum material with Young’s Modulus 70 GPa and material density 2700 kg/m3. Single and double damage cases are induced in connections of the frame as reported in the literature. In the single
Conclusion and future directions
In this study, a two-step method for identifying damage in connections of moment frames has been proposed. In the first step, the potential location of damage in connections has been obtained through SVM leading to reducing the size of damage variables. Then, the accurate location and precise amount of damage in connections have been determined in the second step via DEA. In order to simulate damage in connections, moment frames have been modeled with semi-rigid beam to column connections and
Declaration of Competing Interest
No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer to https://doi.org/10.1016/j.asoc.2019.106008.
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