Data Mining Technology for Structural Control Systems: Concept, Development, and Comparison

Structural control systems are classified into four categories, that is, passive, active, semi-active, and hybrid systems. These systems must be designed in the best way to control harmonic motions imposed to structures. Therefore, a precise powerful computer-based technology is required to increase the damping characteristics of structures. In this direction, data mining has provided numerous solutions to structural damped system problems as an all-inclusive technology due to its computational ability. This chapter provides a broad, yet in-depth, overview in data mining including knowledge view (i.e., concept, functions, and techniques) as well as application view in damped systems, shock absorbers, and harmonic oscillators. To aid the aim, various data mining techniques are classified in three groups, that is, classification-, prediction-, and optimization-based data mining methods, in order to present the development of this technology. According to this categorization, the applications of statistical, machine learning, and artificial intelligence techniques with respect to vibration control system research area are compared. Then, some related examples are detailed in order to indicate the efficiency of data mining algorithms. Last but not least, capabilities and limitations of the most applicable data mining-based methods in structural control systems are presented. To the best of our knowledge, the current research is the first attempt to illustrate the data mining applications in this domain.


Introduction
In recent years, there has been a vast theoretical and experimental investigations in various problems encountered in different structures, from basic structural components (e.g., beams and plates) to complex structural systems (e.g., bridges and buildings). This is due to the fact that structures are built to support a load, namely, static or dynamic loads, incoming from different forces (e.g., tension, compression, torsion, bending, and shear). In this direction, many structures need to be designed to withstand dynamic loads even though they spend most of the time supporting static loads [1,2]. Static loads are those that are gradually applied and remain in

Data mining concept
Data can be defined as any fact, number, or text which can be proceeded by a computer. As the obtained pattern through data mining may be very difficult to find, it is sometimes compared to gold mining in rivers (Figure 1). The term "gold mining" refers to the search for gold in rocks or sand. Data mining is a search for information and knowledge. The origination of data mining traces back to the development of artificial intelligence in the 1950s. The development of data mining is shown in Figure 2.
In general, data mining has two classes which are descriptive mining and predictive mining using various techniques and functions (see Figure 3 and Table 1). The techniques play important roles to obtain effective models from observations. Besides, data mining techniques have also three main groups which are statistical techniques, machine learning techniques, and artificial intelligence techniques. It is noted that each of these techniques has particular algorithms for running the models to get the best solution. For instance, artificial neural network (ANN), Bayesian analysis, ant colony optimization, ICA, support vector machine, principal component analysis, particle swarm optimization (PSO), genetic algorithm, fuzzy logic, regression analysis, clustering, classification, and decision tree are classified under data mining techniques. Furthermore, the functions of data mining are categorized into clustering, prediction, classification, exploration, and association. The purpose of clustering is to divide the samples into groups with related behavior. The numerical prediction activity determines patterns, rules, or models to predict continuous or discrete target values which can also be used for other functions. Classification is used to recognize several rules which can be applied in future work to determine whether a previously unknown item belongs to a known class. Exploration is used to find out dimensionality of an input data, and, eventually, the association activity is used to frequently detect occurring related objects. Based on their particular utilizations in consequence of their assumptions and drawbacks, one or a combination of some of these tasks can be used to find the hidden information [24][25][26][27].  SVM is one of the classification-and prediction-based techniques which was first introduced by Vapnik in 1963 [28]. It works based on learning theory and because of its high accuracy and good generalization capability; it has the potential to produce high-quality predictions in numerous tasks. Therefore, SVM has various  applications which can be found in several areas such as machine learning, data classification, and pattern recognition [29,30]. Basic models of SVM are linear SVM with linear functions and nonlinear SVM with kernel functions. Moreover, the aim of SVM classifier is to determine a separating hyperplane to divide the given data into two classes (i.e., positive class and negative class) in the optimal form. Therefore, the optimal separating hyperplane is determined by solving an optimization problem [31]. SVM has been used in structural control systems. For instance, a SVM-based semi-active control strategy was reported by [32] for the numerical model of a multi-storey structure. In this study, four seismic waves including the El Centro, Hachinohe, and Kobe waves, as well as the Shanghai artificial wave, whose peak ground accelerations were all scaled to 0.1 g, were taken into consideration. As shown in Figure 4, a three-storey shear-type frame structure with dampers was considered as a case study in this work.
The seismic responses of structural top storey with the structure-damper system, structure-SVM system, and no-control device are shown, respectively, in Figure 5. It is seen from this figure that the structure-SVM system model has perfectly learned the control effectiveness of the structure-damper system. This observation indicated that the structure-SVM system model was significantly better than the structure-damper system.
In order to further examine the seismic response reduction of the controlled structure using the present algorithm, the displacement response of every floor under these four seismic waves is shown in Figure 6. It is seen that under the Hachinohe wave, the peak displacement response of every floor, especially the top floor, with the structure-SVM system model, was remarkably smaller than that with the structure-damper system. The authors verified once again that the proposed structure-SVM system model will render better effectiveness than the structure-damper system.
Comparative results of this study demonstrate that general semi-active dampers designed using the SVM-based semi-active control algorithm was capable of providing the higher level of response reduction.

Artificial neural network (ANN)
Artificial neural network, which is a self-organizing prediction-based computational technique, was first proposed in the 1980s. This algorithm can solve many functions through pattern recognition [33]. It also can effectively be used to reconstruct nonlinear relationship learning from training [34]. A typical ANN model has two parts, that is, processing units (neurons) and connections between elements [34], in which neurons are located in layers of the network. A layered ANN structure, called multilayer perceptron (MLP), is one of the most widespread ANN methods. Generally, a conventional ANN has three layers which are input layer, hidden layer, and output layer. ANNs also can be categorized by their network topology such as feed forward and feedback or by their learning algorithms such as supervised learning and unsupervised learning [35].   There are a variety of researches focusing on the application of ANN in structural control systems. For instance, according to reports by [36,37], ANN has a great capacity to improve the functionality of active control systems due to its high pattern recognition capability. It also could be used for semi-active [38,39] and passive damping systems [40]. The following are the review of some related examples which indicate the applicability of ANN in damping systems.
Suresh et al. [36] applied a nonlinearly parameterized neural network as a novel controller scheme for the active control of earthquake-excited nonlinear baseisolated buildings. Numerical simulations were performed on a full-scale numerical test-bed base-isolated building with an isolation system comprising hysteretic lead-rubber bearings. They showed that the proposed approach could achieve good response reductions for a wide range of near-fault earthquakes, without a corresponding increase in the superstructure response. Figure 7 demonstrates a neural network model that was developed by [40] which shows the application of ANN in passive damping devices. In this study, the ANN was employed in order to predict the inelastic demand of structural systems with viscoelastic dampers in terms of peak displacement, effective damping, and effective time period. The authors established that the ANN could be effectively used for new designs as well as for checking the response of any retrofitted structure for the chosen design spectrum. In addition, they concluded that artificial neural networks also were useful in quickly deciding the amount of damping and the number of dampers required to reduce the peak displacement and help in restricting further damage.
A smart active control system, called NEURO-FBG combining fiber Bragg grating (FBG) sensors and neural networks, has been proposed by [41] in a steel building. In this study, an attempt has been made to illustrate the development procedure of the converter and controller by means of "NEURO-FBG converter" and "NEURO-FBG controller." In this regard, the NEURO-FBG smart control system was designed to be a robust and reliable active control system with "smart" performance. To achieve this goal, a specific methodology was proposed comprising three parts, that is, a structural surveillance system, three converters, and a controller (see Figure 8). The analytical results show that the NEURO-FBG system could effectively control the response of the structure and provide a more reliable system than ordinary active control. Later on, the authors verified their method using an experimentation [42]. According to their experimental results, the proposed active control system can be successfully applied to buildings. Figure 9 shows the architecture of an ANN-based real-time force tracking scheme for magnetorheological (MR) dampers, which was applied numerically and experimentally on a five-storey shear frame by [43]. In this study, the forward and inverse MR damper dynamics were modeled by the neural network method using constant and half-sinusoidal current tests. As it can be seen in Figure 9, the ANN modeling was implemented for the forward and inverse MR damper model. It was concluded that the experimental validation of the neural network modeling both the forward and inverse MR damper dynamics showed the accuracy of these models.
A semi-active control strategy that combined a neuro-control system including a multilayer ANN with a back-propagation training algorithm with a smart damper was proposed to reduce seismic responses of structures [38]. A set of numerical simulations was performed to verify the effectiveness of the proposed method.   To aid the aim, two controllers were used, that is, (1) a primary control algorithm based on a cost function, and the sensitivity evaluation algorithm was employed in order to replace an emulator neural network as well as produce the desired active control force and (2) a secondary bang-bang-type controller caused the smart damper to generate the desired active control force, so long as this force was dissipative. It should be noted that cost function is defined as the squared sum of offset between the actual and the desired responses. Therefore, the main purpose was to minimize the cost function during training the network. Figure 10 demonstrates the diagram of control for semi-active neuro-control using smart damper as well as a three-storey building with a single smart damper which was used as a numerical modeling. The authors showed that the proposed semi-active control system using ANN and smart dampers was a promising tool for control of real structures.

Fuzzy logic
Fuzzy logic was proposed by Lotfi Zadeh for the first time in 1965. It has been employed in different applications such as pattern recognition, classification, decision-making, etc. [44]. The basic configuration of a fuzzy technique consists of four important components, which are fuzzification, fuzzy rule base, fuzzy inference, and defuzzification. Fuzzification is a mapping from a crisp input to fuzzy membership sets. The fuzzy rule base has set rules of fuzzy variables described by membership functions. Fuzzy inference is a decision-making mechanism of the fuzzy system. The defuzzifier changes the fuzzy consequences from different rules into crisp values [45]. Fuzzy is a model-free technique for structural system identification, where the most important advantages of fuzzy systems are their high parallel implementation, nonlinearity, and being capable of adapting [46]. Applications of fuzzy logic in SHM are detailed in Table 2.
Adaptive fuzzy control strategy [47], fuzzy gain scheduling [48], semi-active fuzzy logic control system [49], model-based fuzzy logic controller (MBFLC) [50],  optimal fuzzy logic controller [51], fuzzy controller [52][53][54], neuro-fuzzy [55][56][57], genetic fuzzy logic controller (GFLC) [58], fuzzy control strategy based on a neural network forecasting model [59], and wavelet-neuro-fuzzy control [37] are some of the important applications of fuzzy logic in structural control systems. The following examples illustrate the applicability of fuzzy in damping systems. A semi-active fuzzy control system was introduced by [49] to reduce the seismic responses in variable orifice dampers. In this direction, a numerical study was conducted to investigate the effectiveness of the proposed approach. Results revealed that the fuzzy logic controller (FLC) was capable of improving the structural responses. Another semi-active fuzzy control system comprising a semi-active tuned mass damper (STMD) system with variable damping was proposed by [60] to control the flutter instability of long-span suspension  bridges. In this study, the variable damping of the system was chosen through a fuzzy logic controller. The STMD-FLC methodology was applied to increase the flutter wind speed of the test structure which was a suspension bridge. To do so, in order to select the level of semi-active damping ratio, a fuzzy logic feedback controller was incorporated into a closed-loop control system. The displacement and velocity quantities were used as the input to the fuzzy logic controller, and the level of STMD damping ratio was its output for each degree of freedom, namely, vertical and torsional (see Figure 11). The FLC system was designed based on the Mamdani's fuzzy inference method.
In addition, a comparison of the effectiveness of passive TMD and STMD-FLC was carried out in this research, which is shown in Table 2. The table clearly shows the superior performance of semi-active control over the passive control.
The description of the fuzzy input membership function abbreviations is as follows: NL = negative large, NM = negative medium, NS = negative small, ZR = zero, PS = positive small, PM = positive medium, and PL = positive large; and those of the output are as follows: ZR = zero, VS = very small, S = small, L = large, and VL = very large.
Adaptive network-based fuzzy inference system (ANFIS) is a hybrid learning algorithm which combines the back-propagation gradient descent and least squares techniques to generate a fuzzy inference system. The membership functions in ANFIS are adjusted according to a given set of input and output data. The main objective of ANFIS is to integrate the finest features of neural networks and fuzzy systems. Accordingly, the outputs of ANFIS can be seen in two steps, that is, (1) representation of prior knowledge into a set of constraints to reduce the optimization search space from fuzzy system and (2) adaptation of back-propagation to structured network to automate fuzzy control parametric tuning from neural network. Therefore, ANFIS is one of the best trade-offs between neural and fuzzy systems providing smoothness due to the fuzzy control interpolation and adaptability, due to the neural network backpropagation [61].
ANFIS has proven to be an excellent function approximation tool. For example, an ANFIS controller was developed by [61] for reduction of environmentally induced vibration in multiple-degree-of-freedom building structure with MR damper. The systems were excited using two different earthquake random vibration loadings. Figure 12 illustrates the comparison of the displacement response at the top of the structure with and without control under El Centro and Hachinohe earthquakes. The figure shows that ANFIS clearly could reduce the displacement amplitude in both vibration loadings.

Clustering
Clustering is an unsupervised statistical data analysis technique, which is used in pattern recognition, image analysis, and bioinformatics. This method is employed to divide datasets into separated similar subsets (clusters) according to typical patterns identified in the clustering analysis [62]. In order to have a successful clustering, maximum intra-cluster similarity as well as minimum inter-cluster similarity is required. The K-means is one of the most descriptive partitioning clustering algorithms with a quite reliable effectiveness at local optimum. However, it can be employed only to numerical datasets. Furthermore, K-means has poor handling for data prone to noise and outliers [63]. Clustering can also help to decrease the distance between datasets and improve the similarity of datasets in each cluster [64,65].
A combination of fuzzy C-means clustering and subtractive clustering has been developed numerically for nonlinear system identification of a seismically excited building-MR damper system. It was demonstrated from the simulation that the proposed fuzzy model is effective in identifying nonlinear behavior of the building-MR damper system subjected to the 1940 El Centro earthquake. Figure 13 compares the displacement and acceleration responses of the original simulation model with those of the identified model. Note that the original simulation model means an analysis model of the building equipped with an MR damper. As can be seen from the figure, overall good agreements between the original values and the identified model were found in the time histories of both displacement and acceleration responses [66].

Genetic algorithm (GA)
GA, which is one the most powerful optimization-based algorithms, was first proposed by John Holland in the 1970s. In GA, a chromosome is used to determine the solution. The chromosome includes a group of genes that optimize parameters. This algorithm employs a random solution from a current population. Then, the next generation will be created using crossover and mutation operators [67]. In general, GA is an attractive tool to optimize difficult problems due to its benefits such as parallelism, convergence to global optima, adaptation, and no need for the gradient of the objective function. Considering these benefits, GA has been successfully applied in optimal design of TMDs [68][69][70] and multiple tuned liquid column damper (MTLCD) [71], optimization of earthquake energy dissipation system [72], optimization of active control systems in high-rise buildings [73], optimal damper distribution [74], smart control systems [75], etc.  An optimization strategy of hydraulic actuators, that is, an implicit redundant representation (IRR) genetic algorithm with a non-dominated sorting II (NS2) GA, namely, NS2-IRR GA, was implemented numerically by [73] in order to minimize the distribution of control devices in large-scale structures as well as optimize the dynamic responses of structures. It was shown that the proposed NS2-IRR GA-based control system was effective in finding not only optimal locations and numbers of actuators in structures but also minimum responses of the buildings. In the same line, Figure 14, which compares the dynamic behavior of the proposed approach with those of the benchmark control system in reducing displacements of the 20-storey building, clearly indicates the effectiveness of GA in minimizing the displacement/drift responses of the building structure.

Particle swarm optimization
PSO which was first proposed by Kennedy and Eberhart [76] is one of the population-based artificial intelligence optimization-based techniques. The approach was simulated by the social behavior of organisms such as bird flocking to be used as a suitable tool for global optimization [77]. In PSO, a particle represents a potential solution where each particle has two updatable features: position and velocity. PSO is easy to apply and has a great computational capacity. In comparison with other optimization approaches, PSO is more efficient and requires a fewer numbers of function evaluations while giving better or the same quality of results. However, it has some weaknesses such as trapping into local optimum in a complex search space. Besides, the disability to implement a precise local search around a local optimum is another drawback in PSO [78,79].
PSO was applied for optimization of the parameters of a TMD-viscously damped system in [80] including the optimum mass ratio, damper damping, and tuning frequency. The results were calculated by means of three numerical examples for different nonstationary ground acceleration systems to demonstrate the efficiency of the proposed method. To this end, the system was subjected to ground accelerations with different PSO-based power spectra in order to minimize either the maximum displacement or acceleration mean square responses. The authors of this research reported that it was quite easy to program the applications of PSO in practical engineering.
Another method called wavelet PSO-based linear quadratic regulator (WPSOB-LQR) was presented numerically by [81] to find the optimal control force of active TMD via PSO-based linear quadratic regulator (LQR) and wavelet analysis. To aid the aim, PSO was used to determine the gain matrices through the online update of the weighting matrices used in the controller while eliminating the trial and error. Figure 15 shows the time history of displacement response by using predeveloped LQR control method and the proposed WPSOB-LQR approach. As it can be observed from this figure, the displacement was significantly reduced using their proposed method. Moreover, the authors stated that the proposed method was practicable and worthwhile for vibration control of structures.

Conclusion
In this chapter, a brief description of data mining has been made, the most applicable techniques were reviewed, and the applications of machine learning, artificial intelligence, and statistical algorithms in structural control systems have been stated. Furthermore, for each technique, an attempt has been made to present several examples to familiarize readers more in the corresponding field as well as presenting an overall background of the researches done by several investigators worldwide. The following are some of the important conclusions.
Fuzzy, GA, and ANN are the most applicable methods in structural control systems. Among all, fuzzy controllers were the most powerful techniques to solve numerous problems. As a matter of fact, fuzzy algorithm could present uncomplicated and strong solutions for control systems in order to modify uncertainty, such as selecting damping ratios and reducing the responses of structures. ANN was another self-organizing technique which has been used to control and predict  the seismic responses of structures with energy dissipation systems. As far as the ANN was concerned, the local minimum point, overlearning, and the excessive dependence on experience in the choice of structures and types were its inevitable limitations, while SVM could get rid of these limitations and has been successfully applied to time series forecasting. Likewise, SVM could provide some special advantages in the fields of small sample issues and nonlinear and high-dimensional pattern recognition. MATLAB was the main program language which has been used to develop data mining techniques in this area.