Artificial Ground Motions Research Articles

Nonlinear seismic response analysis of long-span railway cable-stayed bridges crossing strike-slip faults

Active faults along railways in the mountainous regions of western China pose significant challenges to bridge safety. To ensure the safe operation of long-span railway bridges under complex geological conditions, this study investigates the synthesis of artificial ground motions for bridges crossing strike-slip faults and analyzes their nonlinear seismic response. First, we develop a theoretical method for simulating high- and low-frequency seismic motions using a finite fault and an equivalent velocity pulse model. Next, using a specific long-span railway cable-stayed bridge as a case study, we construct a nonlinear finite element model with OpenSees software. Finally, we assess the seismic response of key bridge components considering various crossing angles, seismic amplitudes, fault rupture directivity, and fling-step effects. The results show that the crossing angle significantly influences the seismic response, with longitudinal and transverse responses exhibiting opposite patterns. Additionally, the scaling factor of seismic motion significantly affects bridge response. For bridges crossing strike-slip faults, the longitudinal response exhibits a sudden increase in displacement due to instantaneous velocity pulses, while the transverse response shows notable residual displacement influenced by the fling-step effect. However, the critical section curvatures of bridge towers and piers remain within the elastic range across all crossing angles, indicating that controlling large displacement deformations is crucial for the seismic design of bridges crossing strike-slip faults.

Seismic testing and fragility analysis considering material strength uncertainty of 1100 kV GFRP composite power transformer bushing

Nowadays glass-fibre reinforced polymer (GFRP) composite insulators are widely employed in electrical equipment in substations. However, there is a scarcity of reports on seismic qualification of transformer bushings that adopt GFRP insulators. Thereby, this case implements shaking table tests on a 1100 kV GFRP composite power transformer bushing. The study analyses the acceleration responses and dynamic amplification effects, as well as the strain responses. The combined stresses at the vulnerable positions are computed to authenticate the seismic performance. Using a simulation model, the seismic fragility of the transformer bushing considering the material strength uncertainty is assessed and discussed. The results indicate that the GFRP composite bushing meets the requirements of the relevant code and its seismic performance is qualified under an artificial ground motion with PGAs of 0.6 g and 0.8 g. For a given factor of safety of 1.67, the bushing can sustain 0.4 g earthquakes with a failure probability near 0 and 0.8 g earthquakes with a failure probability<50 %. Controlling coefficient of variation of the GFRP material strengths is beneficial to decreasing seismic fragility of the transformer bushing within a specific PGA range. Weibull and Normal distributions for fitting the strength distributions of the GFRP materials have different impacts on the seismic fragility of the bushing, which should be given more attention in seismic design.

A prolegomenon to Design Input Energy Spectra for the Himalayan region

Energy-based design is becoming progressively significant as a new age of earthquake-resistant design unfolds. Thitherto, very little is known about energy-based design in India despite the fact that the Himalayan region is one of the most seismically active regions in the world. Therefore, the current work provides a preliminary analysis of the elastic input energy and equivalent velocity (Vea) spectra for the active regions in the Himalayas. In this regard, the ground motions of Himalayan databases are blended with NGA WEST2 to estimate the Vea spectra, an inertia-independent representation of the input energy spectra. Incipiently, an Artificial Neural Network-based ground motion model (GMM) is developed for Vea spectra based on the predictor variables as magnitude, distance, hypocentral depth and site conditions. Consequently, a Probabilistic Seismic Hazard analysis is performed to obtain the uniform hazard energy spectra for a 2475-year return period. In addition, a Design Input Energy Spectra is proposed for the active regions in the Indian Himalayas. In addition, the relationship between the Vea and pseudo-spectral velocity (PSV) is analyzed to develop a Vea-informed GMM for PSV. Furthermore, the PSA estimated from the Vea-PSV model is compared with the design spectra recommended by the Indian Standard Code of Practice (IS1893-1:2016).

Seismic response prediction using a hybrid unsupervised and supervised machine learning in case of 3D RC frame buildings

The seismic vulnerability assessment represents an important step in monitoring the buildings’ capacity and checking their performance during and after earthquake events. The Nonlinear Time History Analysis (NL-THA) is considered the most reliable method that is used to calculate the exact structural behavior of any building. However, this sophisticated method is known for its complexity, the use of Finite Element (FE) software, and computational time consuming, especially in the case of tall buildings. For that reason, An Artificial Neural network (ANN) is used to develop a new model able to predict the essential Engineering Demand Parameters (EDPs), i.e., the Maximum Base Shear (MBS), the Maximum Inter-story Drift (MIDR) and the Maximum Roof Drift Ratio (RDR). Unsupervised algorithms such as the Principal Component Analysis PCA and the Autoencoder are coupled with the ANN to reduce the dimensionality, improve the dataset quality, and reduce the irrelevant features. More than 192,000 buildings are analyzed using the NL-THA and eighty artificial ground motions (GMs) to generate the dataset. The buildings’ characteristics are generated randomly from the selection range. The results showed that the Autoencoder-ANN model represents the highest performance compared to the PCA-ANN and ANN models. The Autoencoder-ANN model could quickly and accurately predict the seismic responses of unseen ground motions using only the building’s characteristics and the GM parameters without using any FE software.

Shaking table tests and numerical simulations on RC frames retrofitted with friction-damped brace

In this study, the dynamic response of double-story reinforced concrete (RC) space frames retrofitted with diagonally arranged friction damped-brace system was evaluated through shaking table tests. A simplified friction damper was proposed and tested under cyclic loading, later used to retrofit an RC frame. The splice of a conventional steel brace was converted into a friction damper, which requires limited technical expertise on site. Commercially available brake-pads were used as a friction material between the splice plates and bracing elements. An artificial ground motion characterized by a short period, similar to the Korean earthquake histories, was generated and used for the shaking table tests. The tested RC frame half-scaled of existing old structures in Korea. The shaking table tests results demonstrated that the dynamic response of the retrofitted RC frame was improved with reduced drift demands. Additionally, a numerical modelling method for friction damped-brace system was developed, and the dynamic responses of retrofitted RC frame with the proposed friction damper was numerically investigated using OpenSees. The numerical simulation results agreed well with the experimental observations.

Analysis of the Mechanical Characteristics of Tunnels Under the Coupling Effect of Submarine Active Faults and Ground Vibrations

With the rapid development of modern transportation construction, the construction of cross-harbor tunnels has solved the problem of traffic connection between cross-straits, bays and islands. The construction of sub-sea tunnels has technical difficulties such as high difficulty of marine geological survey, close hydraulic connection between strata and seawater, and more developed adverse geology. Based on this, this paper studies the mechanical characteristics of the submarine tunnel under seismic action at the active fault. Firstly, the mechanical model of the universal fault interface is established, and the calculation model of the fault interface is theoretically derived by the method of vibration mechanics, and the influence of the change of the strength of the contact surface and the stiffness of the surrounding rock on both sides of the fault on the transfer coefficient is obtained. Secondly, based on the ground motion input method of two-dimensional homogeneous half-space field, the relevant program of viscoelastic artificial boundary ground motion input is written by MATLAB program, which lays the foundation and premise of load input for mechanical response calculation. Finally, the outcomes of the tunnel parameters and the interplay between the tunnel and the surrounding rock on the cracking of the tunnel lining shape and the mechanical response of the cross-fault sub-sea tunnel underneath seismic motion are mentioned, and it is concluded that the increase in seismic intensity for different seismic intensities under the sea floor has an essentially constant proportion to the increase in acceleration of the seismic response; the seepage effect under the sea floor for the tunnel lining structure reduces the seismic response displacement, velocity and The seabed seepage for the tunnel lining structure reduces the peak seismic response displacement, velocity and acceleration by about 20–35%.

Experimental and numerical analyses of seismic behaviors of L-shaped unreinforced masonry walls

This study investigates the seismic behavior of L-shaped unreinforced concrete-block masonry fence walls. Using a large-scale shaking table, the walls are subjected to uniaxially artificial ground motions that gradually increase in intensity, and the out-of-plane response and failure mode are analyzed. The seismic behavior is then simulated by LS-DYNA using a finite element model under identical conditions as the shaking table tests. The validity of the numerical model is evaluated by comparing the linear response and failure mode of the tests with those of the simulations. Practical modeling techniques and calibrated material model parameters that facilitate reliable simulation results are also presented. The numerical model and techniques are useful in determining the geometrical features required for earthquake-resistant fence walls, such as the maximum permissible width and height as well as the appropriate height- and width-to-thickness ratios, depending on wall support conditions.

Artificial Neural Networks for seismic demand prediction of a single degree of freedom

This paper proposes using an artificial neural network (ANN) to estimate and predict the seismic demand of Single Degree of Freedom (SDOF) systems. Our methodology entails the production of a comprehensive dataset containing SDOF and earthquake characteristics. Nonlinear Time History Analysis (NL-THA) is performed on a randomly generated SDOF system using thirty-one artificial ground motions (GMs) matched to the EuroCode-8 (EC8) response spectrum to train the ANN model. To assess the performance of the ANN model, we compare the Incremental Dynamic Analysis (IDA) curves, the median IDA curve, and the 3D fragility surface in a case study. This analysis assists in determining the precision and dependability of the predicted maximum displacement of the SDOF system. The results showed a remarkable reduction in processing time without losing prediction accuracy. . It was concludedthat the ANN-based method can be used as an alternative for the current method for estimating the performance points and the fragility assessment of buildings.

Effects of pulse-like ground motions on tunnels in saturated poroelastic soil for obliquely incident seismic waves

It has been widely recognised that near-fault ground motions can be distinctly different from far-fault ground motions, in terms of their amplitudes and spectral characteristics, and there are a number of studies investigating the effects of near-fault ground motions on the structural response. However, only a few studies focus on underground tunnels, and most of them consider vertically incident seismic waves, neglecting the wave passage effect which is critical for long tunnels. This paper investigates the consequences of near-fault pulse-like ground motions on the seismic tunnel response, with an example of a tunnel embedded in saturated poroelastic soil. The input motions are represented by obliquely incident P1 waves, and the wave passage effect along the longitudinal direction is considered by a 2.5D modelling technique. The seismic tunnel response for near-fault pulse-like and far-fault ground motions is compared. Additionally, artificial ground motions, which have consistent acceleration response spectra with the near-fault pulse-like ground motions, but without velocity pulses, are generated to gain further insight into the contribution of velocity pulses. It is shown that the near-fault pulse-like ground motions can noticeably increase the tunnel internal forces, due to large seismic energy associated with the velocity pulses. For pulse-like ground motions with similar acceleration response spectra, the fling-step velocity pulse can be more detrimental to the tunnel than the forward-directivity velocity pulse. Moreover, the amplification effect of the near-fault pulse-like ground motions on the tunnel internal forces tends to be more prominent for large vertical angles of incidence, highlighting the significance of considering the oblique incidence case for seismic design.

Deterministic Seismic Hazard Analysis to Determine Liquefaction Potential Due to Earthquake

The great rocking of building structures and the occurrence of liquefaction in water-saturated soil on river banks are generally caused by earthquake shaking. The waves generated by the earthquake are the main cause of the shaking. In order to show the effect of ground motion earthquake shaking on the response of structures and liquefaction processes, it is necessary to analyze the structure and liquefaction as well as the time history of artificial earthquake ground motions. An artificial time history for liquefaction analysis can be developed based on spectral matching to the target spectrum generated by a deterministic seismic hazard analysis. Therefore, the time history recovered from the analysis can be said to be derived from a deterministic procedure. The analysis of liquefaction with time history aims to see the potential for liquefaction in the Palu region of Central Sulawesi by developing the time history of the bedrock. The time history of the bedrock is then spread over the ground surface. The propagation of time-historical waves to the ground surface can cause liquefaction events in the soil layer. It was found that liquefaction occurred in the Palu region, especially in the Anutapura Hospital building. No other liquefaction potential analysis studies were found in the region. Doi: 10.28991/CEJ-2023-09-05-012 Full Text: PDF

Seismic response mitigation of prefabricated industrial equipment structural frames through a hybrid isolation system

For reducing the excessive acceleration response of the critical equipment in a type of industrial equipment structural frames under strong earthquakes, a hybrid isolation system (HIS), incorporating linear natural rubber (LNR) and lead rubber (LR) bearings, is proposed. The efficiency and reliability of the HIS are verified through a series of full-scale shaking table tests on two prefabricated industrial moment resisting frames (MRFs), with respect to a corresponding fixed-base system (FBS). The structural dynamic characteristic and seismic performance of the two types of MRFs, i.e., reinforced concrete structure (RCS) and composite concrete-filled steel tube structure (CCFSTS), are examined both with the HIS and FBS subjected to a range of seismic intensities. The test results demonstrate the superior performance of the HIS in controlling transient acceleration response under near-fault, far-field and artificial ground motions. The average peak acceleration reduction coefficients (PARCs) of the HIS range between 75.60% and 79.51% in the two considered MRFs along two horizontal directions, with a strict satisfaction on the peak acceleration response for normal operation of the critical equipment. Also, the hysteretic behavior of the HIS is stable and controllable during the earthquake excitations. The peak transient displacement of the HIS is satisfactory, and the residual deformation is negligible even under the maximum considered earthquake (MCE) excitations. Besides, components of the two MRFs are undamaged during the whole test. Thus, with the capacity of protecting the acceleration-sensitive equipment and structural components, the proposed HIS possesses a great prospect in enhancing the structural resilience.

Assessment of seismic acceleration demands on nonstructural components in moderately ductile RC frame buildings designed according to NBC 2015

This paper presents an extensive investigation of the seismic demands on acceleration-sensitive nonstructural components (NSCs) attached to reinforced concrete moment-resisting frame buildings with limited ductility and designed according to the National Building Code of Canada. A total of four benchmark structures with varying heights are considered in this study. Linear and nonlinear time-history analyses were performed using artificial ground motions compatible with Montreal site Class C uniform hazard spectra having 2% and 10% probabilities of being exceeded in 50 years. Seismic acceleration demands on NSCs were evaluated by assessing the horizontal height factor Ax, the component dynamic amplification factor Ar, and the component force factor Sp compared with various building code provisions. The overall acceleration demands of NSCs are discussed, and a corresponding optimized Sp profile is proposed to improve the estimation of the seismic force demands on NSCs at the rooftops of buildings located in moderate seismic zones.

Development of a Control Algorithm for a Semi-Active Mid-Story Isolation System Using Reinforcement Learning

The semi-active control system is widely used to reduce the seismic response of building structures. Its control performance mainly depends on the applied control algorithms. Various semi-active control algorithms have been developed to date. Recently, machine learning has been applied to various engineering fields and provided successful results. Because reinforcement learning (RL) has shown good performance for real-time decision-making problems, structural control engineers have become interested in RL. In this study, RL was applied to the development of a semi-active control algorithm. Among various RL methods, a Deep Q-network (DQN) was selected because of its successful application to many control problems. A sample building structure was constructed by using a semi-active mid-story isolation system (SMIS) with a magnetorheological damper. Artificial ground motions were generated for numerical simulation. In this study, the sample building structure and seismic excitation were used to make the RL environment. The reward of RL was designed to reduce the peak story drift and the isolation story drift. Skyhook and groundhook control algorithms were applied for comparative study. Based on numerical results, this paper shows that the proposed control algorithm can effectively reduce the seismic responses of building structures with a SMIS.

Effects of the Transverse Deck-Roadbed Pounding on the Seismic Behaviors of the Prefabricated Frame Bridge

Pounding effects on prefabricated frame bridges are not clear, which may influence seismic behaviors a lot in some cases. Prefabricated frame bridges are emerging structures designed to solve the problem of difficult land acquisition in highway expansion and reconstruction, the deck of the prefabricated frame bridge is adjacent to the original roadbed in the transverse direction, so the pounding potential exists under the earthquake ground motions. In this study, the artificial ground motions of the different seismic intensities are selected to carry out the nonlinear time history analyses, and the pounding effects on the prefabricated frame bridge are evaluated based on the pounding forces and the components’ seismic response. It is found that the pounding effects are not obvious in all cases; some energy can be dissipated in the pounding process, which is also limited to some extent. Finally, the influences of the gap distance and seismic intensity are investigated according to the parameter sensitivity analysis. The results indicate that the gap distance and the seismic intensity are the two important factors related to the pounding effects, the seismic response of the components will decrease when the pounding effects are obvious, and the transverse deformation of the deck cannot influence the stress state of the superstructure.

Numerical investigation on the seismic performance of a RC framed building equipped with a novel Prestressed LEad Damper with Straight Shaft

This study aims at assessing the use of a novel damper, which is called the Prestressed LEad Damper with Straight Shaft (or PS-LED), for the seismic rehabilitation of RC framed buildings. This device provides high energy dissipation by the friction activated between a lead core and a shaft and achieves a high specific output force by preloading the lead during the assembly. In order to show the effectiveness of the PS-LED device for the retrofit of existing buildings, a RC structure designed according to past codes that ignored seismic actions is retrofitted with the PS-LED system considering two different damage targets: (i) in the first case, the structure is retrofitted in order to behave elastically under the design earthquake; (ii) in the second case, a partially dissipative behavior of the structure is conceived, with activation of plastic hinges, and limited and reparable damage. In order to assess the suitability of the design procedure, non-linear static analyses are performed on the upgraded building, showing a satisfactory agreement between the seismic performance and the design target. Non-linear dynamic analyses are further carried out considering a suite of bidirectional artificial ground motions with response spectra matching on average the target spectrum according to the Italian Building Code for the life-safety limit state. Finally, a comparison is performed between the performances of the building retrofitted with the PS-LED device and the building retrofitted with a conventional steel hysteretic damper (SHD), demonstrating that the PS-LED, thanks to its superior damping capacity, limits the increase in internal forces that usually affects frames equipped with SHDs, reducing the need of local strengthening of the columns and foundations and consequently the total cost of the seismic rehabilitation.

Study on the multi-criteria seismic mitigation optimization of a single pylon cable-stayed bridge across strike-slip fault rupture zones

Bridge structures across active faults suffer the serious threats from large surface deformation and velocity pulses. This study focuses on developing a multi-criteria optimizing method and investigating the damping effect of the optimized damper system on a cable-stayed bridge across a strike-slip fault. A simplified baseline corrected method is adopted to recover the static offsets in near-fault records and the improved record-decomposition incorporation method is modified to produce artificial across-fault ground motions. A single pylon cable-stayed bridge across a strike-slip fault is taken as the case bridge and the refined nonlinear numerical model is established in OpenSees. The conventional multi-criteria decision making (MCDM) theory is improved by introducing new function forms and a control parameter to assess the best fault-crossing angles of the case bridge. The improved MCDM method is integrated with the beetle antennae search algorithm to optimize the damper system of the case bridge. Finally, the influence of fault-crossing angles and earthquake parameters (permanent displacements and ratios of maximum to permanent displacement) on the damping effect of the optimized damper system are investigated. The results indicate that the cable-stayed bridge reaches optimal seismic performance when the fault-crossing angle is around 90° (75°-105°) as both the biaxial nonlinearity of the pylon and the risk of the girder unseating are reduced. The damper system is efficiently optimized by the proposed method, and the displacement and force demand of the case bridge are balanced. Both the fault-crossing angles and earthquake parameters are observed to have considerable influence on the damping effects. More specifically, the damping effect on most seismic responses is optimized when the fault-crossing angle approaches 90° (60°-120°). As the permanent displacement increases, the damping effect on the pier-girder relative displacement is significantly reduced and the damping effect on the pier moments is moderately decreased. Moreover, the damping effect is improved for all the seismic responses as the ratios of maximum to permanent displacements increase, with the exception of transverse displacement.

Effects of Ground Motion Duration on Seismic Damage of Bridge Isolation Bearings Based on Friction SDOF System

It is generally perceived that ground motion duration has an effect on structural seismic response and damage, despite the neglect of current seismic codes. Based on friction SDOF systems, this paper investigates the duration effect of ground motions on seismic responses and damage of sliding bearings. Ground motions are divided into long-duration (LD) and short-duration (SD) cases, taking the significant duration of 25[Formula: see text]s as the boundary. Each case consists of natural records and spectrally equivalent artificial ground motions to decouple duration from other earthquake characteristics. Results from response history analyses implicate that duration has hardly any effect on seismic responses of the system exhibiting an approximate linear elasticity. Nevertheless, for systems with distinct frictional nonlinearity, selecting LD ground motions as seismic inputs usually leads to a conservative result. By performing incremental dynamic analysis (IDA), nonlinear systems in SD cases bear 10% higher damage risk than those in LD cases without considering the influence of temperature rise. The same is true for systems with a small friction coefficient of 0.005 when earthquakes are in the low intensity range. It was also found that damage exceedance probabilities of these small friction coefficient systems are almost unaffected by the duration as the peak ground acceleration increases to more than 0.6[Formula: see text][Formula: see text]. When the effect of temperature rise caused by friction is considered, the damage exceedance probability in LD cases is higher than SD cases. The damage probability of friction SDOF system under LD earthquake will be underestimated without considering the influence of temperature rise.

A benchmark shaking table test on the seismic responses of an extra‐large LNG storage tank

AbstractIn recent years, many large‐scale liquefied natural gas (LNG) storage tanks have been built all over the world. Due to their high constructional cost and important functions to the public, the academic and engineering communities are very concerned with the operational safety of these important infrastructures once subjected to potentially disastrous actions, that is, earthquakes, typhoons, tsunamis, and so forth. This work presented a benchmark test in evaluating the aseismic performance of extra‐large prestressed reinforced concrete (RC) LNG storage tanks. A 1:14 scaled model of the prototype LNG tank was designed and constructed for shaking table tests. Two recorded and two artificial earthquake ground motions with peak ground acceleration (PGA) up to 1.2g were selected successively as seismic inputs to the tank. The acceleration, displacement, shear force, and strain responses of the model structure were presented, analyzed, and discussed in detail. It was found that due to the differences in the frequency spectra, the seismic excitations have distinct influences on the responses of the tank model. In particular, the wall‐roof junction was detected as the weakest part of the outer tank, and the filling water had non‐negligible effects on the overall seismic responses of the tank. Verified finite element simulations were also presented as supplements to the experimental study. Some suggestions were made with the aim to improve the designs of LNG storage tanks.

Seismic resonant metamaterials for the protection of an elastic-plastic SDOF system against vertically propagating seismic shear waves (SH) in nonlinear soil

The paper explores the key mechanisms that govern the dynamic interaction between resonant metamaterials (consisting of multiple unit cells embedded in the soil, with horizontally vibrating internal masses) and an existing nonlinear structure on nonlinear soil. Elastic behavior of the soil and of the SDOF system, representing the structure, is also investigated for comparison. The Real-ESSI Simulator is employed to develop in-plane (2D) finite element (FE) models, and an extensive parametric analysis is conducted to evaluate the influence of key parameters on the protective efficiency of resonant metamaterials. Both artificial and real ground motions are used as seismic excitation, vertically propagated through the soil as shear waves (SH), employing the Domain Reduction Method (DRM). Two protective mechanisms are identified. The first mechanism is related to the inertial interaction of the metamaterials with the surrounding soil, namely, it is the out-of-phase resonant oscillation of the internal metamaterial masses with respect to the soil at periods close to the natural period of the structure. The maximum reduction in structural response is achieved when the resonant period of the metamaterials is equal or a bit larger than the effective period of the structure. The second mechanism is related to the kinematic interaction of the metamaterials with the surrounding soil, namely, the presence of empty unit cells (no internal masses) in the soil next to the structure creates a protective “shadow” zone. This kinematic interaction mechanism becomes effective when the wavelength of the incoming seismic waves is comparable to the size of the metamaterials, and at the same time, the period of the waves is close to the natural period of the structure. When both soil and structural nonlinearities are considered, the effect of metamaterials remains always beneficial, and their action is localized, making them practically harmless to neighboring structures.

Improved Hybrid Method for the Generation of Ground Motions Compatible with the Multi-Damping Design Spectra

ABSTRACT Spectra-compatible artificial ground motions are used extensively in the time history analysis of nuclear power plants. Owing to reasons such as the dense controlling frequency points and stringent requirements for the number of small response points, it is difficult for the conventional matching methods to generate artificial ground motions that are highly compatible with multi-damping design spectra. In this paper, to resolve the problems of high precision and robustness, an improved hybrid method for constructing a multi-parameter adjustment curve in the time domain is proposed. Different from artificial intelligence methods, the improved hybrid method is a deterministic iterative method that combines the advantages of the simulated annealing algorithm (SAA) and the time domain adjustment method. The SAA is used to determine the optimal weights of the corrective time histories of all the damping ratios at a specific frequency, which controls the influences of the corrective time histories on the response spectra. Subsequently, based on the optimal weights, the artificial ground motion is adjusted in the time domain to reduce the fitting error of all the damping ratios at a specific frequency. Moreover, the multi-damping design spectra matching problem of frequencies and damping ratios is simplified to a one-dimensional problem of frequencies using the SAA. Numerical examples are presented to demonstrate the versatility of the proposed improved hybrid method.