A Hybrid Particle Swarm Optimization and Genetic Algorithm for Model Updating of A Pier-Type Structure Using Experimental Modal Analysis

Conventional design of pier structures is based on the assumption of fully rigid joints. In practice, the real connections are semi-rigid that cause changes in dynamic characteristics. In this study, quality of the joints is investigated by considering changes in natural frequencies. For this purpose, numerical and experimental modal analyses are carried out on related physical model of a pier type structure. When numerical results are evaluated, natural frequencies generally do not match the expected experimental results. Uncertainties in different aspects of engineering problems are always a challenge for researchers. The numerical models which are constructed on the basis of highly idealized scheme may not be able to represent all of the physical aspects of the physical one. For this study, determination of percentage of semi-rigid joints is considered as an optimization problem based on the numerical and experimental frequencies. Probabilistic sensitivity analysis is also used to determine the search space. A new technique of optimization problem is solved by a combination of smart particle swarm optimization (PSO) and genetic algorithms, and a complicated and efficient system for model updating process is introduced. It is observed that the hybrid PSO-Genetic algorithm is applicable and appropriate in model updating process. It performs better than PSO algorithm, considering the good agreement between theoretical frequencies and experimental ones, before and after model updating.


Introduction
Investigation on the behavior of the coastal structures needs an accurate study on the complicated dynamic conditions arise from the harsh marine environment. Inadequate knowledge of the dynamic conditions in different situations may lead to major structural damages. About the coastal structures, in view of the unexpected aspects arising from the marine environment, there are numerous uncertainty parameters which can influence the accuracy of the methods which employ the dynamic behavior concepts. These uncertainties have a great effect on the dynamic behavior of the structures.
Uncertainties in engineering problems can be attributed to three distinct environmental, structural and practical factors (Gupta and Manohar, 2001;Schüttrumpf et al., 2008;Bradner et al., 2010;Batou, 2015). Among coastal structures, piers play the most important transportation key role in both normal and hurricane conditions. These struc-tures are subjected to enormous forces such as the strong waves, winds, and currents . Since pier's deck includes the main part of the structure mass, the connections of pile to deck may have an important role in structural strength (Seiffert et al., 2015). Due to this reason, in the present research, the uncertainties in the percentage of the semi-rigidity of pile-deck joints are investigated by employing the experimental and numerical aspects. In recent years, several researchers have studied the effects of the semi-rigid connections on structural responses (Hadidi and Rafiee, 2015;Moussemi et al., 2016;Qian et al., 2017;Koriga et al., 2019). Bayat and Zahrai (2017) investigated the seismic performances of the steel frames defined as mixture of rigid and semi-rigid connections. Kim et al. (2016) studied the performance of beam-to-column connections used in the middle-low rise buildings. The moment capacities of the failure modes were calculated and compared with the test results. Soleimani and Behnamfar (2017) proposed a three-parameter tangent inverse equation for the moment rotation relationship of semi-rigid steel beam-to-column connections. Feizi et al. (2015) investigated the seismic performances of steel moment-resisting frames with mixed use of rigid and semi-rigid connections to control the base shear. Kohoutek (1998) studied the semi-rigid joint using non-destructive dynamic in a rigid joint. The results of an experimental modal analysis were introduced and the effect of the joint on the dynamic response was evaluated using dynamic deformation. Türker et al. (2009) presented a method to determine the semi-rigid connections of the steel structures with consideration of the changes into the dynamic characteristics. Zhang et al. (2018) investigated the effect of semi-rigid connection in behavior of steel frames. They proposed multi-spring component model for evaluating the rotational stiffness of semi-rigid connections. A non-parametric model of random uncertainties for structure dynamic reduced model was presented by Soiz (2000). Mojtahedi et al. (2019) investigated the effect of uncertainty parameters for a marine structure using a fuzzy logic system. It was found that the involvement of the uncertainty effect in the numerical modeling can increase the success rate of the used algorithms. Conventionally, in most of the engineering processes such as design, modal analysis, and health monitoring, all joints are considered fully-rigid or pinned. However, this assumption is not practically correct and it can also cause serious consequences. The semi-rigid joints affect the lateral displacement, P-Δ effect, dynamic parameters etc. (Yu and Shanmugam, 1986;Chen and Lui, 1987;Pogg, 1988). ASD (AISC, 1989) introduced three types of joint: rigid framing, simple frame, and semi-rigid frame. LRFD (AISC, 1993) suggested two fully restrained and partially restrained joints. Ozturk and Catal (2005) investigated the dynamic response of semi-rigid joints by a linear elastic rotational spring. The comparison of the results for the considered frame responses indicated that semirigidity of the joints can increase vibration period, especially in low modes. Dynamic behavior of coastal piers has been studied by some researchers (Verdure et al., 2005;Iwan and Huang, 1996;Schüttrumpf et al., 2008;Verdure et al., 2005).
However, identifying the percentage of semi-rigidity of the pile-deck joints shows that there is an urgent need for further research so that more detailed guidelines will be provided on the dynamic characteristics of the considered structures. In this paper, the effect of the uncertainties arise from the semi-rigidity of the structural connections on the updating process is investigated, based on the measured dynamic responses of the structure. For this aim, a scaled model of a coastal pier like structure is conducted to determine the percentage of the semi-rigidities. The model was examined by experimental modal analysis to extract structural responses such as the mode shapes and natural frequencies.
At the second step, a finite element (FE) model was developed by ABAQUS software package. In this FE model, a linear elastic rotational spring was modeled for simulating semi-rigidity of the joints. At the next step, a theoretical FE modal analysis code was prepared in MATLAB software. Using this code, the related equations of semi-rigidity percentage extracted. Finally, the amount of the semi-rigidity is optimized, based on the numerical updating and experimental results and probabilistic sensitivity analysis. The capability of the hybrid PSO-Genetic (HPSOGA) and Particle Swarm Optimization algorithm (PSO) is evaluated to solve the related optimization problem, and numerical model is updated. The observed results imply that the ideal full rigid connections for a real structure cannot be considered as a true assumption. Especially, because of the harsh environment and related uncertainties of the coastal structures, they should be analyzed with the assumption of semi-rigidity of connections via a suitable technique. This study proposes a method which is able to determine the percentages of joint semi-rigidities to correctly update the numerical model of considered structures.

Experimental modal analysis
2.1 Model specification A physical scaled model was built considering the dimensional proportion of a common pier like structure. The general view of the setup and instrumentation of the modal testing are shown in Fig. 1. The scaled model was a steel frame with 39.5 kg in weight consisting of 9 piles welded to the bed and the deck to ensure the rigid connections, as much as possible. Physical and geometric properties of the piles and deck are given in Table 1. Piles were made of steel pipes with the outer diameter, thickness and length being 40, 5 and 600 mm, respectively. Piles distance ratio (S/d) is 3.75 (where S is the gap distance between two consecutive piles and d is the pile's diameter) and model frame contains horizontal and diagonal brace members with 10 mm in diameter. Fig. 2 demonstrates a sample of recorded data of acceleration and related coherence function that were recorded during one implemented test set of this work. The conditions of these figures (the values close to 1) demonstrate the appropriateness of the data recording, during the process of the experimental tests.

Modal testing
The modal analysis determines dynamic intrinsic properties of a system based on the natural frequencies, and mode shapes, which can be used to create a mathematical model of the system dynamic behavior. In this study, the modal test was implemented using the external excitation which was enforced by means of an electro-dynamic exciter (type 4 809) with a force sensor (AC20, APTech) driven by a power amplifier (model 2 706), all made by Bruel and Kjaer. The excitation signal could be applied using a time series generated by a signal generator system. The loads were applied into a fixed point on the middle part of the legs which was marked as number 7, as shown in Fig. 3. The instrumentation included 2 light uni-axial accelerometers (4 508 B&K) for response measurement and locations of the selected sampling points (SL1, SL4, SP1, and SP2, as shown in Table 2).
Accelerometers are placed in X and Y directions to record the structure responses in both directions, simultaneously. In order to measure the structure responses, four nodes on the deck and main piles are considered. As the number of desirable nodes is more than available data logger channels and sensors, measurement is done in 50 steps using movable accelerometers method. The natural frequencies of the experimental test and related mode shapes were gained by ME'scopeVES software via implementation of signal processing on imported frequency response functions into ME'scopeVES software. The software is a powerful tool used for estimating modal parameters by curve fitting a set of measurements, such as frequency response functions. The modal analyzing process is achieved by applying a white noise up to the range of 1.6 kHz to the model in frequency domain. Data are recorded by attaching the accelerometers to all nodes of the experimental model in both Xand Y-directions. Natural frequencies of the experimental model are shown in Table 3, and the first and third mode shapes are illustrated in Fig. 4. Only the outer columns have been considered for the schematic figures of modelled structure and related mode shapes in ME'scope to ensure the clarity.

Numerical analysis
3.1 Numerical model specification Numerical modal analysis was performed using finite    element method done by both ABAQUS software and MATLAB coding. An initial 3D-Finite element model of the studied structure was generated using ABAQUS software package for vibration analysis according to the considered boundary conditions. This software uses techniques including finite element concepts which can analyze different types of structures such as the frames, trusses, space frames based on the specifications of the structural components such as the steel joints, members etc. In this study, element SHELL S4R and B13 was used for modeling deck and piles, respectively. They are elements with 6 degrees of freedom and 4 and 2 nodes, respectively. A general view of the model geometry and the conditions of joint numberings of the prepared model for numerical analysis are shown in Fig. 3. The modeling process was performed by assuming all connections as full rigid to obtain the initial numerical modal results. The numerical mode shapes and the initial natural frequencies are shown in Table 4  3.2 Space frames and structural dynamics by finite element modelling Un-damped dynamic equation of motions for multi degree of freedom can be written as follows: where, M, K, and D denote, mass matrix, stiffness matrix, time-dependent acceleration and displacement vectors, respectively. Fig. 6 shows the typical member i of a space frame including the rotations of joints of j and k. The and planes are the principal planes of bending.
The stiffness matrix of local axes is composed of three 6×6 matrixes as follows: where r 1 and r 2 are and , respectively. A, L, E, , , and are area, length, Modulus of elasticity, and moments of inertia, respectively. The consistent mass matrix for local directions contains the sub matrices as Eqs.    (Weaver and Johnston, 1994).  (5), where and r g are mass density and radius of gyration, respectively.
Regarding the flexibilities, an elastic structure can have an infinite number of natural modes of vibration. By discretization via the finite element method, the resulting model will have a finite number of nodal degrees of freedom and modes of vibration. The concept can also be developed by the normal mode method. As an advantage, this method requires only the significant modal responses of the dynamic analysis. For this purpose, the eigenvalue problem can be considered and produced as Eqs. (6) and (7): where , , and are the i-th and J-th eigenvalues and eigenvectors, respectively. To take advantage of the diagonalization process, related equation can be produced via multiplication of equation of motion by as follows: Based on the generalized mass and stiffness matrices, the generalized displacements and accelerations in original coordinate are related to those in principal coordinates. The most common choice of the set of generalized displacements is that for which the mass matrix is transformed to identity matrix. In this study, the numerical modal analysis was implemented by employing the MATLAB software coding based on solving an eigenvalue problem, considering the structural dynamics using finite element theories. For more detailed theoretical information readers can refer to Weaver and Johnston (1994).

Numerical modelling of the semi-rigid connections
In fact, due to the uncertainty arises from the welding conditions of connections, the assumption of full-rigidity may not be completely correct. Therefore, considering a percentage of rigidity in the pile-deck joint within the dynamic characteristics of the structure is of vital importance. The amount of the joints rigidity can be determined according to the moment-rotation curves that are obtained by experimental data curve regression. Resistance moment depends on the amount of rotation directly related to the rigidity of the joint. Different types of the moment−rotation curves ( ) have been developed by Chen and Lui (1987). A deformed element with semi-rigid connections is considered as shown in Fig. 7. Where, , and are deformation of element, deformation of connection and total deformation, respectively. The deformation of connection depends on its flexibility including rigidity of connection and the bending moment , as follows: is the field of the displacements for the dynamic analysis that can be defined by form functions and the nodal displacements , , and , as follows (Filho et al., 2004): The stiffness index of connections at the ends of the element can be presented as follows (Filho et al., 2004;Ozturk and Catal, 2005): The stiffness matrix of the element considering the semi rigidity of connections can be represented as follows: Alireza MOJTAHEDI et al. China Ocean Eng., 2020, Vol. 34, No. 5, P. 697-707 701 where B ij can be defined as: Also, parameter P i (i=1 and 2) is the fixity factor of semi rigid connection at the end of the element and is in relation to the stiffness index R i as follows: (14) For this study, the elastic linear rotational spring and related formulas were used to model and simulate the semi-rigidity of joints, using ABAQUS and MATLAB software. The effects of the semi-rigidity can be evaluated with consideration of element stiffness matrix in local coordinates as: θ θ where is the matrix of semi-rigid coefficients and multiplied by stiffness matrix of the connected elements to the deck of the structure. The parameters of were calculated as defined by McGuire et al. (1999) and Türker et al. (2009).

Optimization algorithm
For the sake of identifying the precise updated percentage of semi-rigidity, an optimization problem was conducted as an objective function subroutine done by the hybrid PSO-Genetic and basic PSO with the modal analysis process, simultaneously. Designed optimization problems consist of several main components. A proper definition of each component leads to a better result, with high precision. The objective function of this study was defined based on the determined accurate and real percentage of semi-rigidity of pile-deck connections. Accordingly, the decision variables and related search space were described.

PSO algorithm
PSO is a meta-heuristic and population based stochastic optimization algorithm developed by Kennedy and Eberhart (1995). The main concept of this algorithm was inspired by the social behavior of bird flocking. PSO simulates the flock of birds which communicate during flights.
In this algorithm, the entire population is called a swarm with each individual in the swarm called a particle. Each particle uses two very important properties of intelligence and speed to search for problem space. Particles movement depends on several factors including the particle current position, the best position that particle has ever visited, particle velocities and the best position that particles have ever visited. Each i-th particle is composed of three vectors of x i , v i and which are the particle current position, particle velocity, and the best position that particle has ever visited, respectively. is a set of coordinates that shows the particle current position. In every step, the algorithm is repeated and is calculated as a problem answer. If this situation is better than the previous answers, it would be saved in . Where is the objective function value in and is the objective function value in . It is necessary to save for the next comparisons. The algorithm will repeat to gain a better and in each repetition new and are obtained. The best position that has been found by the particles is shown as which is selected by comparing values of from the values. The amount of the objective function in is shown as . Particles movement for covering the search space can be written as: where w, and r 2 are inertia coefficient, random and positive numbers with uniform distribution in [0, 1], respectively. Parameters c 1 and c 2 are also two positive constants.

Hybrid PSO-GA
A genetic algorithm is a population based stochastic global search technique that applies the theory of the evolution to solving the complex optimization problem. This algorithm is based on the evolutionary ideas of natural selection and genetic process. GA exploits new and better solutions by using three main operators including selection, mutation and crossover. The selection operator is one of the most important processes of GA algorithm because it significantly affects solution convergence. The GA uses probabilistic selection for selecting chromosomes to generate new population. Another important operator is crossover that chooses a locus and exchanges the subsequences before and after locus between two chromosomes to create offspring. Therefore crossover is one of the most critical GA operations to exploit the solution space. The mutation operator mutates the gene for making more population to achieve best solution. In GA the crossover and mutation rates determine the tradeoff between exploitation-and-exploration in GA search.
The motivation of hybridization is an approach to combine the advantages and eliminate the weaknesses of PSO and GA algorithms for increasing its performance (Ali and Fig. 7. Deformed semi rigid connection (Filho et al., 2004).
Tawhid, 2017). The main idea in HPSOGA is to combine the advantage of social behavior of PSO with the local search ability of GA. By hybridization of PSO and GA, a more efficient algorithm is obtained that have more balance between exploration and exploitation features. This method, like other algorithms has been stated from the initialization phase. Initialization phase is the same as basic PSO, where positions and corresponding velocities of particles are generated randomly in search space. Based on the PSO rules, particles updated their positions and evaluated the objective function. Some particles are selected and GA operators, crossover and mutation, are applied to them. Then the objective function is evaluated for offspring. The population is ranked on the basis of fitness values. The position of population updated by PSO principles and this process repeated. The process of HPSOGA can be summarized as follows: (1) Start PSO with generation initial positions and velocities of particles: • Evaluating objective function and calculating best individual and global fitness; value; • Updating positions of all particles; • Ranking the particles based on objective function values.
(2) Start GA with calculating the fitness of each chromosome: • Applying crossover; • Applying mutation; • Evaluating objective function for all offspring; • Combining population; • Ranking population; • Selecting new population; • Replacing population.
(3) Updating positions and velocities of particles based PSO rules: • Update personal and global best objective function fitness.
(4) If stopping criteria not satisfied go to Step (2) else go to Step (5).
(5) End The performance of proposed method is sensitive to PSO and GA parameters. To determine the appropriate values of the parameters, it is necessary to perform numerical simulation with specific rigidity percentage in each node. The results with these rigidity percentages are extracted and inserted as an input to objective function. Then the algorithm is executed with different parameters and the most suitable parameters are calculated with trial and error. The best parameters of HPSOGA are shown in Table 5. The fre-quency-based objective function was measured to minimize the difference of calculated frequencies and defined as follows: where refers to experimental natural frequencies which were obtained by experimental modal analysis. Correspondingly, refers to natural calculated frequencies by the theoretical modal analysis concepts. In point of fact, the algorithm must be trained to obtain closer to by applying the indexes of the rigidity percentage at the nodes of the connected pile elements to the deck joints. In Eq. (18) the parameter n refers to the number of the first considered natural frequencies of the structure. Here, the decision variables are the parameter of the joint rigidity percentage (P i ). Also, the related search space of optimization problem is determined by using probabilistic sensitivity analysis.

Finite element model updating process
Because the finite element modelling is considered as a process based on the simplified assumptions, it is not possible to achieve all the features of a real structure. Therefore, there will be a difference between dynamic experiments, due to control model validity especially for natural frequencies, mode shapes, and analytical model results . The results shown in Tables 3 and 4 can prove this fact. The results of the exact investigations of the different modeling parameters justify that the observed differences depend on the uncertainty arising from the assumption of ideally full rigid connections and experimental errors. Therefore, the analytical model is corrected based on the dynamic measurement results (experimental tests), in a process known as the finite element model updating.

Probabilistic sensitivity analysis
Probabilistic sensitivity analysis is one of the most important tools to investigate the influence of different factors on the structural behaviors and demonstrates the parameter uncertainty in a decision problem. In this section, the probabilistic sensitivity analysis is used to investigate the effect of semi-rigid connection of pile-to-deck (P 1 ) on the dynamic behavior of the pier. Since the percentages of semi-rigid are positive values, the log-normal distribution is used for modeling of uncertainty in the rigidity of connections. Monte Carlo simulation is used for sensitivity analysis. Initially, the influence of individual rigidity connections on the dynamic response was investigated by Monte Carlo simula-  Eng., 2020, Vol. 34, No. 5, P. 697-707 tion. For example, the variations of first and third natural frequency are shown in Fig. 8 for connection 3. Also, the variations of the first and the second natural frequency are shown in Fig. 9 for connection 5. As shown in these figures, the first natural frequency is increased by increasing the rigidity connections percentages in connection 3 and 5 linearly. Also, the second and the third natural frequency decreased by increasing rigidity in connection 3 and 5 respectively.
In the second step, the Monte Carlo simulation is per-formed by changing the rigid parameters of all connections simultaneously. Variations of the natural frequency versus the mean of all rigidity connections are shown in Fig. 10. The average of rigidity in all connections is selected to display the variation of natural frequency because it is not possible to display the graph in 9 dimensions form. In this regard, log-normal distribution is considered to all rigidity connections, then the mean of rigidity connections and corresponding natural frequencies are calculated in each step.
The simulation results also showed that the variations of   the rigidity in connection affected significantly on the first and third natural frequencies. According to Fig. 10, the variations of the first and second natural frequency versus the mean of the rigidity change more linearly. As can be seen in this figure, increasing in the rigidity connectivity does not always increase the natural frequency. In this type of structure, the effect of rigidity on the second and third frequencies must be considered in order to avoid any possible dangerous.
According to the results of the probabilistic sensitivity analysis shown in Figs, 8−10, the choice of a range from 0.8 to 1 is appropriate for rigidity of connections for updating finite element model. Because in this range, the experimental natural frequencies are well covered. Therefore, the algorithm's search space is limited to this interval.

Solving optimization problem
As mentioned before, the updating process of this study was done by using the natural frequencies to define the objective function of the optimization problem with variables of the indexes of the semi-rigidity of connections, via the PSO and also HPSOGA algorithms. Based on the probabilistic sensitivity analysis results, the search space is limited to 0.8 to 1 for decision variables. In order to investigate the reliability of the proposed method, 50 simulation are considered for model updating. The robustness of predicted parameters is assessed by comparing experimental and computed frequencies and their coefficient of variation (COV). Based on the solved optimization problem and the determined percentage of rigidity of the pile-deck connections, the studied structure and its connections were modeled numerically using the elastic linear rotational springs. The spring stiffness was determined based on the measured rigidity percentage and Eq. (14). The obtained amounts of the rigidity percentages and the related results of the spring stiffness are shown in Table 6.
According to the results of Table 6, the amount of computed rigidity percentages bay PSO and HPSOGA of Node 1 differed from the full-rigid assumption, by approximately 12.7% and 12.1%, respectively. In Node 6 the rigidity percentage was calculated approximately 88.3% by PSO algorithm and 89.8% by HPSOGA, which is different from a full rigid joint by approximately 11.7% and 10.2%, respectively. As the calculated results imply, there are not any fully rigid connections among all of the joints. The highest rigidity percentages were calculated by PSO at Nodes 3 and 9 by 94.1% and 92.9%, respectively. Also, the highest rigidity percentages were calculated by HPSOGA at connection 9 by 93.1%. Coefficient of variation is presented in Fig. 11 for each connection. Low COV of the predicted rigidity connections indicates the low scattering of the predicted parameters in model updating and optimization process. Fig. 11 illustrates that the results of HPSOGA were less scattered than PSO algorithm. Therefore, the number of simulations for the same results is higher for this algorithm. Thus, the performance of HPSOGA can be higher than PSO algorithm.
Numerical and experimental frequency values are shown in Table 7, before and after model updating. The COVs of first twelve natural frequencies are shown in Fig. 12. The convergence function curves for simulation 8 and 45 are also shown in Fig. 13. Based on the convergence diagrams, it is observed that the HPSOGA algorithm has the higher convergence rates than the PSO algorithm. The reason for this rapid convergence is due to more balancing between exploration and exploitation features. In addition, HPSOGA   algorithm uses a larger population due to crossover and mutation operators that can cover more areas of the related search space.

Conclusions
This paper investigates the percentage of semi-rigidity of the structural connections to consider the effect of uncertainty in qualities of rigidity of connections on structural dynamic responses of a pier like structure by numerical and experimental modal analysis to achieve an efficient manner for the model updating. For this purpose, the determination of the percentage of the semi-rigidity was formed based on a developed hybrid particle swarm optimization and genetic algorithms, probabilistic sensitivity analysis and the theoretical modal analysis. The following conclusions can be drawn.
(1) The probabilistic sensitivity analysis could limit the search space of updating process, in turn lead to increase in the efficiency of considered algorithms. Also, the probabilistic sensitivity process emphasizes that the dynamic behaviour of the structure is highly dependent on the percentage of rigidity of connections.
(2) While optimization-based model calibration has been studied previously in the literature, the simultaneous treatment of sensitivities analysis and uncertainties in rigidity of connections within the optimization framework of a real physical complex space framed structure as an experimental study has yet to be investigated. Also, the considered approach can contribute to the efforts of strategies development in computer-aided engineering applications through the complex experimental projects.
(3) The semi-rigidity calculation results indicate that the suppositions of ideal full rigid connections for a real structure cannot be considered as a true assumption. For the stud-ied model, there were considerable percentage differences in comparison to full rigid connections. On the other hand, the observed numerical and experimental natural frequencies had a suitable convergence that showed the efficiency of the purposeful method, according to the updated model results.
(4) In fact, the present method is able to determine the percentages of joint semi-rigidities to correctly update the numerical model of considered structures. The assumption of the semi-rigidity of connections can increase the structural flexibility and leads to a decrease in natural frequencies and an increase in displacements. Generally, because of the dynamic and related uncertainties of environment of the coastal structures, they should be analyzed with the assumption of semi-rigidity of connections with a suitable method like the presented one and a semi-rigid model should be used to obtain more accurate results for reliable design purposes.
(5) The results also show that hybrid PSO-Genetic algorithm performed a little better than PSO algorithm but performance of both considered algorithms are not much different. In comparison of two algorithms, the new hybrid method showed more feasible for coupling two considered optimization algorithm and also required less iteration number in some cases. Therefore, according to the physics of pier type structure, it has been seen that training an intelligent method using a swarm based optimization algorithm, in comparison to an evolutionary based optimization algorithm like genetic, is more adaptable with considered updating process.
It is necessary to mention that during the real operational conditions, there would be other numerous uncertainties which can influence the accuracy of the updating procedure and are remained unsolved for this study and they must be considered as the topics of the future research.