Bridge Model Research Articles

Mechanism of noise reduction caused by thickening top plate for high-speed railway box-girder bridge

For the high-speed railway concrete box-girder bridge, thickening the top plate can effectively reduce the structural noise radiation caused by moving trains. However, the noise reduction mechanism for thickening top plate has not been investigated. This mechanism is systematically studied in this paper by employing a train-track-bridge spatially coupled dynamics model and an acoustics boundary element model of the box-girder bridge. The results demonstrate that the top plate is the dominant noise source for the concrete box-girder bridge. Thickening top plate can significantly reduce the noise radiation capacity of the box-girder bridge, mainly through three mechanisms: (1) reducing the local modal shapes and vibrations of top plate, (2) decreasing the acoustic radiation efficiency, and (3) redistributing the train-induced vibration in the bridge. Furthermore, these three aspects collectively determine the total amount and spatial distribution of the noise radiation from the box-girder bridge due to moving trains. It is crucial to comprehensively these three aspects for the low-noise design of box-girder bridge.

Influence of Hydrodynamic Effect on Dynamic Response of Bridge with Complex Piers Submerged in Reservoir

In order to clarify the influence of hydrodynamic on dynamic response of bridge with complex piers submerged in reservoir, based on the continuous beam of a 4-column pile column frame pier in Xiaolangdi Reservoir of Yellow River, taking 4-column pile column frame pier and bridge as the object separately, the numerical analysis model of bridge (pier) - water interaction is established by ANSYS. The flow around deep-water piers is analyzed. For the single pier (SP) and the pier of the bridge (BP), the dynamic responses of different flow velocities, water depths and wave heights and the combined action are studied. The research shows that detouring flow analysis shows that velocity field and pressure field of each column are asymmetric. Specifically, for this bridge, due to the columns interfere with each other, the velocity difference of 1#, 4# column is more obvious than that of 2#, 3# column. Maximum and stability values of the dynamic response of SP and BP increase with the increase of flow velocity and depth. Specifically, as the water flow velocity increases, the maximum response of the dynamic response increases linearly, while the stable response of the dynamic response increases in the form of a quadratic curve. When the water depth does not exceed 50 m, the maximum and stable values of the dynamic response gradually increase in the form of a quadratic curve. When the wave acts alone, the dynamic response of SP and BP is the largest at the wave crest and the smallest at the wave trough. The maximum dynamic response at the wave crest and trough increases with the increase of wave height. With the increase of water depth, the dynamic effects of waves on SP and BP are more significant. Under the combined action of wave and current, the dynamic response of SP and BP increases with the increase of wave height and water depth. For different flow velocities, the maximum value of dynamic response at wave crest increases with the increase of flow velocity, and the maximum absolute value of dynamic response at wave trough decreases with the increase of flow velocity. Dynamic response under the combined action of wave and current is not the superposition of the dynamic response under the separate action of wave and current. The maximum value of dynamic response appears in wave crest and wave trough, indicating that the current does not change the action of wave field, and the wave still plays a leading role. Specifically, the influence of water on the dynamic response of BP is: pier bottom bending moment > pier bottom shear force > pier top displacement and the influence of water on the dynamic response of SP is: pier bottom bending moment > pier top displacement > pier bottom shear force.

Quantitative analysis of the importance and correlation of urban bridges and roads in the study of road network vulnerability

The city development is closely related to the performance of the transportation network system. Bridges and roads are important parts of the transportation system, and are also inseparable components of the transportation network. However, the effect of the correlation between bridges and roads on the network system has not been studies thoroughly in the literature. Therefore, it is necessary to analyse the vulnerability of the road network when both bridges and roads are involved. In this paper, the urban road network is modeled into the form of network connection and node, based on the analysis of the related research results of road network vulnerability in the literature. Taking the urban roads at all levels as the connection and the transportation hubs (including bridges) as the nodes, the paper puts forward the corresponding measurement indexes and calculation methods, and establishes the importance and correlation analysis model of roads and bridges in the urban road network. At last, the model is applied to the road network which is 5 × 3 km2 besides Yangpu Bridge of Shanghai for verification, the importance and correlation of specific roads and bridges in the analyzed urban road network are calculated, which provides a certain basis for dealing with various emergencies leading to the decline of urban road network vulnerability. In this paper, the importance analysis of urban road network is extended to the bridge correlation analysis, so that the proposed model of the vulnerability assessment of the urban road network system is more suitable for the increasingly demand of road and bridge construction in China, and provides a certain basis for dealing with the decline of road network vulnerability caused by various emergencies.

Conflation of modal strain energy, spectral finite element, and machine learning techniques for damage detection in multi-span steel girder bridges with variable sections

A new approach is proposed to detect micro and small damages in multi-span bridges constructed with variable sections by combining modal strain energy and spectral finite element through the use of machine learning techniques. The traditional finite element methods are inefficient in detecting and estimating structures' micro-damages. Therefore, wave propagation-based methods must be applied. Micro-damages can be modeled through the spectral finite element method, widely adopted in wave propagation simulation. Among the frequency-based methods used in damage identification, the modal strain energy is more sensitive, especially in complicated structures. However, this method is difficult to apply to steel girders with variable sections and different support conditions. By combining the modal strain energy and the spectral finite element and applying the support vector regression method, the location and severity of damage in steel girders could be accurately identified to overcome the difficulties of detection in complicated elements. To improve the ability of the support vector regression method, in the damage severity estimation, it was combined with feature selection. To evaluate the proposed method's ability, first, an element of the beam- type, with the characteristics of a spectral finite element, is defined in the OpenSees software. To assess the accuracy of the defined element in detecting micro-damages, a tested numerical model was adopted to measure the accuracy of the provided element. Next, to detect small damages, the model of the steel girder bridge with the defined element was prepared, and the modal properties of the structure were extracted. Due to the change in cross-section along each girder, the modified modal strain energy-based damage index (β) equation was used in the subject model. By applying the damages of different severities in steel girders in single and multiple damage scenarios, the modified damage index β was calculated. With the damage indexes calculated in the different scenarios and applying the machine learning method, the severity of damage was estimated. The obtained results indicate that this proposed method is accurate and satisfactory for detecting and estimating micro and small damages with high accuracy in bridges with variable section girders.

Numerical comparative study on seismic response of half-span and full-span scaled models of a floating type cable-stayed bridge

This study compares the results of numerical simulations of half-span and full-span cable-stayed bridge models based on the seismic response of the pylons and main girders subjected to earthquake loads. The half-span model represents the most critical condition of the bridge during the construction phase, while the full-span model represents the bridge in operational phase. The three-dimensional finite-element modeling of the two bridge models uses data from the longest existing cable-stayed bridge in Indonesia which was scaled down geometrically to 1/160, using Midas CIVIL software. The Kobe earthquake record from the PEER Strong Motion Database was used in this study by applying the spectral matching method to modify its acceleration according to the location of the existing bridge being analyzed. This study also examines the influence of the directional effects of earthquake load relative to the longitudinal axis of the bridge, namely 0, 45, and 90 degrees. The results of the analysis show that for the half-span bridge model, the maximum acceleration occurs at the top of the pylon due to earthquake excitation at 90 degrees direction, with an amplification factor of 4.658, while the amplification factor in full-span bridge conditions is only 2.44. In addition, in both the half-span and full-span bridge models, the largest acceleration amplification factor occurs in the main girder that is caused by earthquake excitation at 90 degrees direction. The largest transverse displacement occurs at the free ends of the main girder, but not in the full-span model. The results of the study indicate that during the detailed design process the designer has to consider the effect of earthquake on the strength and stability of the bridge during construction especially if the balanced cantilever method applies.

Influence analysis of the connective elements failures on the road bridges steel reinforced superstructures service reliability

The paper considers the influence issues of connective elements failures, in particular flexible pin stops, on the road bridges steel reinforced superstructures service reliability. The authors have formulated possible criteria for the superstructure failure both for the first and the second groups of limit states, and also developed scenarios of connective elements exclusion from the structures operation, that are modeling the failure of individual connective elements in the operation process. For five finite element models of road bridges steel reinforced superstructures a numerical experiment on modeling of the connective elements exclusion from the operation of the structure was carried out. The calculation results for each scenario and for the partial scenario realization levels were analyzed in terms of possible superstructures failures as a whole. Numerical experiment results have shown that at the exclusion of a separate small group of connective elements increases the maximum stresses in the over-supported beams sections by up to 3 %, and further development of the connective elements disconnection scenario can lead to an increase in stresses by 20 %. It is concluded that for existing steel reinforced superstructures the risk of superstructures failure under normal operating conditions due to disconnection of connective elements is low, even in the case of almost unlikely complete disconnection of all connective elements. Nevertheless, the exclusion from operation of connective elements may be more critical in cases of abnormal bridge structure operation or in cases of significantly lower engineering reserves of the structure in terms of strength and stiffness.

Model updating of in‐service bridges using multidisciplinary research ‐ case studies in Spain

AbstractThis paper presents several experiences focused to create and update accurate numerical models of ageing bridges in Spain. The experimental campaigns included integration of various NDT technologies such as laser scanning, ultrasounds, etc., combined with vibration‐based methods such as Operational Modal Analysis. From these multi‐source data it was possible to create an accurate numerical model of each structure, which was lately subjected to a calibration using the actual dynamic response of the structure. Thus, the updated structural model presents the same behaviour as the real construction, offering a powerful tool to more accurately predict the safety level of the structure. On the other hand, structural assessments based on reliability analysis has been proved to improve the quality and accuracy of safety analysis due to the consideration of the possible deviations presented in the parameters of a structure. These works were compiled as case‐studies in Spain within IM‐SAFE project.

A Frequency-Based Ground Motion Clustering Approach for Data-Driven Surrogate Modeling of Bridges

A Frequency-Based Ground Motion Clustering Approach for Data-Driven Surrogate Modeling of Bridges

Influence of flaw distribution on tensile behavior of Engineered Cementitious Composites (ECC) based on flaw probability model

The high ductility of Engineered Cementitious Composites (ECC) is attributed to the internal fibers’ bridging effect during matrix cracking, where the distribution of strength in components is crucial for ductility design. Starting from fracture mechanics, this paper proposes a method based on the bridging model to convert flaw sizes into fracture strength in an ECC system. The distribution of flaws in the components is implemented using the Weibull function. By incorporating a crack tracing algorithm, the tensile behavior of components under different flaw distributions is calculated. The effectiveness of the proposed model, which considers flaw distribution, is verified through the comparison between the simulated and experimental data. Furthermore, the simulation results indicate that moderate adjustment on the flaw distribution in components can greatly improve the corresponding tensile ductility without compromising the strength. The research outcomes benefit to provide technical supports for the optimization design of material ductility.

Calibration procedure of Discrete Element Method (DEM) parameters for wet and sticky bulk materials

The downtimes associated with blockage events in the materials handling sector have prompted the mining industry to optimise its operations to maximise the profitability of fines and lump products. These blockage events are caused by materials with a high clay or moisture content typically referred to as Wet and Sticky Material (WSM). Numerous methods are commonly used to prevent such blockage events, however, in the majority of cases, they are often too late to prevent the downtime of the system. The Discrete Element Method (DEM) is commonly used to predict and visualise the bulk material flow. DEM is capable of replicating the flow of non-cohesive granular materials with reasonable accuracy, however, when cohesive materials are considered the mechanism becomes much more complex. With the advancement of computational power over the last few decades, it is now more practical to simulate WSMs into DEM.This paper evaluates the capability of three cohesion models to simulate WSMs; the Simplified Johnson-Kendall-Roberts (SJKR) model, the Easo Liquid Bridging model and the Edinburgh Elasto-Plastic Adhesion (EEPA) model. A calibration procedure is proposed where the parameters for each cohesion model are discussed in detail. A series of calibration simulations with systematic parameter variation is undertaken to define a set of calibration matrices. These matrices allow the formation of a parameter database, used for the simulation of on-site applications to optimise plant geometry and other operational parameters. Finally, the numerical model was validated using a lab-scale vertical impact testing facility. Individually, in a transfer chute application, it was determined that none of the 3 cohesion models were suited to WSMs; the SJKR and Easo liquid bridging models were unable to replicate the behaviour, and while the EEPA model was able to replicate the behaviour, extensive solve times deemed it impractical for industrial applications. These limitations were overcome through the coupling of the SJKR and Easo Liquid Bridging models.

Study on the buffeting response of a long-span truss arch bridge during construction based on a large-scale full bridge model wind tunnel test

The buffeting response of long-span truss arch bridges has become a key factor in the cantilever construction phase. It is essential to study the wind-resistant performance of arch bridges in typical construction stages. In this study, the buffeting displacements and buffeting forces were investigated based on a 1:40 scaled full bridge model wind tunnel test. Three wind attack angles and seven wind yaw angles were considered in the test. The test results show that the maximum lateral buffeting displacements of the cantilever end and the buckle tower top occur at a wind yaw angle between −15 and 15°. Finite-element analysis was performed to investigate the vibration mitigation measures of the arch bridge during the maximum cantilever construction stage. Finally, we propose some recommendations to alleviate the buffeting response of the buckle tower. The results of our study reveal that setting two symmetric wind resistance cables with an angle >20° between the cable direction and the vertical direction is useful in reducing the transverse buffeting displacement of the buckle tower. This study provides new insights into the buffeting response and vibration reduction of long-span truss arch bridges during cantilever construction.

Stochastic analysis and dynamic reliability of the heavy-haul train–bridge system based on direct probability integral method

In this paper, a heavy-haul ballasted track–bridge interaction model is established by the finite element method in matrix representations, and their interaction to the train is achieved by the wheel–rail contact. A new direct probability integral method (DPIM) is introduced to achieve the stochastic analysis and reliability assessment of the train-ballasted track–bridge interaction (TTBI) system. Besides, the accuracy of the train-ballasted track–bridge model is validated by the field measurement. The probability characteristics of the dynamic behavior of the system are compared between DPIM and sophisticated PDEM, to show the accuracy and efficiency of the stochastic analysis method. The results demonstrated that the efficiency is improved by 1–2 orders of magnitude in terms of stochastic post-processing. Furthermore, the influences of random factors, e.g., track irregularity, axle loads and bridge parameters, etc., on the dynamic behavior of system are investigated by the proposed method, and the time-dependent reliability is presented with the aid of the extreme distribution events. The results indicate that the train axle load, running speed and variability of parameters have remarkable effects on dynamic performance. Besides, the failure probability of the bridge is very small attribution to the higher allowable threshold (e.g., mid-span displacement), but the safety of train operation decreases with the increase of vehicle speed especially under the critical speed of resonance.

Numerical study of seismic performance of steel-concrete composite rigid-frame bridge with precast segmental CFDST piers crossing fault-rupture zones

Although seismic performance of bridges crossing fault-rupture zones has been studied in recent two decades, there is still no effective solution to mitigate the hazard of fault-crossing effect. Recently, a new type of post-tensioned precast segmental (PTPS) concrete-filled double skin steel tube (CFDST), known as PTPS-CFDST column, has been proposed and verified to exhibit excellent performance with respect to seismic resilience. Moreover, PTPS-CFDST columns can accommodate torsional deformation through joint slip and are thus considered as a promising structural solution for bridges crossing fault-rupture zones. This study aims to investigate the performance of a steel–concrete composite rigid-frame bridge (SCCRFB) with PTPS-CFDST piers subjected to across-fault ground motions through numerical simulations. Two detailed three-dimensional (3D) finite element (FE) bridge models are developed using the explicit FE code LS-DYNA. In particular, Bridge 1 uses the new PTPS-CFDST pier, while Bridge 2 serves as a reference model with monolithic CFDST piers. Two types of across-fault ground motions with strike- and dip-slip mechanisms are used as seismic inputs, and the influence of fling-step is parametrically investigated. Structural responses, including the global seismic responses, seismic damages, energy absorption, and local joint slip and opening, are systematically discussed. The numerical results indicate that, compared to the monolithic CFDST piers, PTPS-CFDST piers exhibit advantages in terms of seismic resilience, with lower damage and outstanding self-centering performance, which facilitates post-earthquake recovery after experiencing across-fault ground motions. This study provides valuable references for the seismic design of bridges with PTPS-CFDST piers crossing fault-rupture zones.

Review of Wind-Induced Effects Estimation through Nonlinear Analysis of Tall Buildings, High-Rise Structures, Flexible Bridges and Transmission Lines

The nonlinear effects exhibited by structures under the action of wind loads have gradually stepped into the vision of wind-resistant researchers. By summarizing the prominent wind-induced nonlinear problems of four types of wind-sensitive structures, namely tall buildings, high-rise structures, flexible bridges, and transmission lines, the occurrence mechanism of their nonlinear effects is revealed, providing cutting-edge research progress in theoretical studies, experimental methods and vibration control. Aerodynamic admittance provides insights into the aerodynamic nonlinearity (AN) between the wind pressure spectrum and wind speed spectrum of tall building surfaces. The equivalent nonlinear equation method is used to solve nonlinear vibration equations with generalized van-der-Pol-type aerodynamic damping terms. The elastic–plastic finite element method and multiscale modeling method are widely employed to analyze the effects of geometric nonlinearity (GN) and material nonlinearity (MN) at local nodes on the wind-induced response of latticed tall structures. The AN in blunt sections of bridges arises from the amplitude dependence of the aerodynamic derivative and the higher-order term of the self-excited force. Volterra series aerodynamic models are more suitable for the nonlinear aerodynamic modeling of bridges than the polynomial models studied more in the past. The improved Lindstedt–Poincare perturbation method, which considers the strong GN in the response of ice-covered transmission lines, offers high accuracy. The complex numerical calculations and nonlinear analyses involved in wind-induced nonlinear effects continue to consume significant computational resources and time, especially for complex wind field conditions and flexible and variable structural forms. It is necessary to further develop analytical, modeling and identification tools to facilitate the modeling of nonlinear features in the future.

Study on the pier bottom self-centering seismic isolation structure of the high-pier continuous rigid frame bridges

Four seismic isolation specimens were designed, fabricated, and subjected to physical loading tests to enhance the seismic performance of a high-pier continuous rigid-frame bridge. A finite element model of the seismic isolation structure of the high-pier was established using numerical simulation software. The entire bridge model was established based on the multi-scale modeling method to investigate the seismic response of the high-pier continuous rigid frame bridge under different seismic waves. The results indicate that the seismic isolation pier has self-centering and energy dissipation capabilities. The seismic isolation pier has satisfactory energy dissipation capacity and ductility when the ratio of the long-axis and short-axis radii is 1.5. The results of the finite-element simulation corresponded well with the experimental results. Significant damage occurred to the concrete at the bottom and corner of the pier, and the reinforcement did not reach its yield strength throughout the loading process. Therefore, measures must be implemented to ensure the seismic performance of the structure. The pier bottom self-centering seismic isolation structure effectively absorbs shocks, as evidenced by reduced absolute acceleration and relative displacement at the pier top, decreased shear force and bending moment at the pier bottom, and minimized girder displacement. It was recommended that the ratio of the long-axis and short-axis radii be adopted as 1.5–2.0 and that the pier height be selected as 60 m–100 m. These results provide a reference for the research and applications of this type of structure.

Emergency Department Bridge Model and Health Services Use Among Patients With Opioid Use Disorder

Little is known about the effectiveness of bridge clinics as transitional care programs for people with opioid use disorder in emergency departments (EDs). We assessed the effect of bridge clinic referral on health services use among patients with opioid use disorder identified in the ED. We used data for individuals aged 18 years and over with active opioid use disorder and no history of medication for opioid use disorder who were administered medication for opioid use disorder while in the ED between January 2013 and August 2022. Bridge clinic referrals started in January 2021. Eligible patients after this date comprised the intervention group. The usual care group included eligible patients before bridge clinic implementation, who were a 1:1 propensity score matched to intervention patients. We estimated risk differences and 95% confidence limits for linkage to long-term care, ED use, and inpatient admission within 120 days of the index ED visit. Our study population comprised 928 observations after matching. Patients referred to the bridge clinic had a higher risk of linkage to long-term care (risk differences=25%; 95% confidence limits: 20%, 30%), higher risk of ED use (risk differences=7.5%, 95% confidence limits: 1.6%, 13%), and lower risk of inpatient admission (risk differences= -1.9%, 95% confidence limits: -5.9%, 2.1%). Inpatient admission increased among patients with serious mental illness but decreased among patients without serious mental illness. Our overall results suggest that bridge clinic referral increases linkage to long-term care. Nevertheless, qualitatively different effects on inpatient admission between patients with and without serious mental illness warrant consideration of unmet needs among patients with serious mental illness.

Experimental and numerical investigation of the mechanical behavior of a cable-stayed bridge with shell-shaped pylons

A novel cable-stayed bridge (CSB) with shell-shaped pylons was first proposed, of which the shell-shaped pylons were uniquely composed of five concrete-filled steel tube (CFST) pylon arches (PAs) and curved circular hollow steel transverse braces. To investigate the force transmission mechanism of this new type of CSB, a static loading test of a 1:25 scale model of the whole bridge and finite element analysis (FEA) of the prototype bridge were performed. The results showed that under the action of vehicular load the shell-shaped pylon and main girder jointly shared the load effect in a distribution ratio of 1:9, and the stress levels of the pylon arch in the middle (PAm) and the pylon arch immediately next to it (PAn) were much greater than the outermost pylon arch (PAo), and the maximum stress occurred at the bottom section of PAs. However, the location where the maximum stress occurred under permanent load would shift to the junction section of the curve and the straight segment of the PAs. Meanwhile, the stress levels of PAm, PAn, and PAo were almost equal under the temperature load, and the maximum stress occurred at the apex of the arch. Furthermore, the refined FEA results of the steel–concrete composite pylon pedestal showed that there were obvious stress concentrations at the steel tubular intersecting joints of the PAm and PAn and the connection area between the connecting steel plate and the steel tube in the pylon pedestal. Nevertheless, the pylon pedestal still behaved elastically under the ultimate limit state.

Lateral vibration suppression of highway bridge by using frequency modulated particle damper in earthquake environment

In order to study the seismic control effect and mechanism of particle damper in the transverse structure of highway’s bridge, a 1:20 scale model of a typical highway bridge is designed and manufactured, and a frequency modulated particle damper is designed and manufactured, which can be used in the test model. The seismic simulation vibration array test is carried out on the model bridge before and after the particle damper is set. By changing the filling rate, particle material, particle size and installation position of the particle damper, the power spectral density at the middle or top of the beam steel column is measured, and the total energy response of the steel column structure is calculated. The influence and law of the particle damper on the vibration amplitude of the steel column are explored. The test results show that: the proposed frequency modulated particle damper does not appear particle accumulation phenomenon in the test; it has better damping effect on the transverse seismic response of the main beam of the scale model bridge, and can reduce the peak displacement response of the main beam. The energy response value is 1.016 kg (m/s2)2/Hz.

Study on dynamic impact factor of girder bridges due to vehicle load model

The dynamic effects of moving vehicle on bridge are generally treated as withstand static loads that are recommended an increment by dynamic impact factors (IMs) (or dynamic amplification factors) in many design codes, that are a function of either the span or the first flexural natural frequency of the bridge. The value of the IM will relate to safe and economical in new bridge designs, evaluate recommendation and operation of bridges. Due to the bridge-vehicle interaction model, previous studies have shown that the calculated IM from field measurements could be higher than the values specified in design codes. Currently, studies on IM often focus on using interaction models with multi mass vehicles move on bridge that are increasingly similar to real models. This study develops a 2D three-axle vehicle–bridge model to analysis the dynamic response of the girder bridge subjected to moving loads consider to some vehicle parameters with the each axle is modelled in two masses, each mass is connected to a spring and a damping corresponding to the suspension and tire. In addition, depending on the stiffness parameters of the suspension and tires of the analyzed vehicle model, the IM results of this study are different from those of some authors and the bridge design rules. Based on the dynamic analysis of the bridge under the vehicle loading consider the stiffness of tire and suspensions, the calculation of the IM needs to be considered more carefully in the process of designing new bridges or existing bridges.

Time-Domain Finite Element Model Updating for Operational Monitoring and Damage Identification of Bridges

The well-known limitations of modal system identification methods have led to a broad exploration of alternative solutions for operational monitoring and damage diagnosis of structures. This study presents a time-domain Bayesian finite element model updating approach to jointly identify the vehicular loads and finite element modeling parameters of bridges using the vibration data and the location of vehicles traversing the bridge as input. A Bayesian model updating is devised and verified through a series of case studies based on numerically simulated data from a prestressed reinforced concrete box-girder bridge model. Damage states are defined for concrete degradation and delamination, steel corrosion, and loss of prestressing force. Ten different damage scenarios, encompassing the range from minor localized to major distributed damage, are examined. The responses of the damaged bridge are simulated under random traffic scenarios. The acceleration responses, along with the location of the vehicles on the bridge, are used for jointly estimating the model parameters and vehicular loads. The estimated model parameters are then used to infer the location and extent of damage within the bridge. The results show the successful performance of the proposed approach in a numerically simulated environment.