Radial Basis Surrogate Model Integrated to Evolutionary Algorithm for Solving Computation Intensive Black-Box Problems

For design optimization with high-dimensional expensive problems, an effective and efficient optimization methodology is desired. This work proposes a series of modification to the Differential Evolution (DE) algorithm for solving computation Intensive Black-Box Problems. The proposed methodology is called Radial Basis Meta-Model Algorithm Assisted Differential Evolutionary (RBF-DE), which is a global optimization algorithm based on the meta-modeling techniques. A meta-modeling assisted DE is proposed to solve computationally expensive optimization problems. The Radial Basis Function (RBF) model is used as a surrogate model to approximate the expensive objective function, while DE employs a mechanism to dynamically select the best performing combination of parameters such as differential rate, cross over probability, and population size. The proposed algorithm is tested on benchmark functions and real life practical applications and problems. The test results demonstrate that the proposed algorithm is promising and performs well compared to other optimization algorithms. The proposed algorithm is capable of converging to acceptable and good solutions in terms of accuracy, number of evaluations, and time needed to converge.

Robust Control of a Dynamic Model of an F-16 Aircraft with Improved Damping through Linear Matrix Inequalities

This work presents an application of Linear Matrix Inequalities (LMI) for the robust control of an F-16 aircraft through an algorithm ensuring the damping factor to the closed loop system. The results show that the zero and gain settings are sufficient to ensure robust performance and stability with respect to various operating points. The technique used is the pole placement, which aims to put the system in closed loop poles in a specific region of the complex plane. Test results using a dynamic model of the F-16 aircraft are presented and discussed.

Effect of Varying Diets on Growth, Development and Survival of Queen Bee (Apis mellifera L.) in Captivity

Keeping in view the increasing demand, queen of Apis mellifera L. (Hymenoptera: Apidae) was reared artificially in this experiment at varying diets including royal jelly. Larval duration, pupal duration, weight, and size of pupae were evaluated at different diets including royal jelly. Queen larvae were raised by Doo Little grafting method. Four different diets were mixed with royal jelly and applied to larvae. Fructose, sugar, yeast, and honey were provided to rearing queen larvae along with same amount of royal jelly. Larval and pupal duration were longest (6.15 and 7.5 days, respectively) at yeast and shortest on honey (5.05 and 7.02 days, respectively). Heavier and bigger pupae were recorded on yeast (168.14 mg and 1.76 cm, respectively) followed by diets having sugar and honey. Due to production of heavier and bigger pupae, yeast was considered as best artificial diet for the growing queen larvae. So, in the second part of experiment, different amounts of yeast were provided to growing larvae along with fixed amount (0.5 g) of royal jelly. Survival rates of the larvae and queen bee were 70% and 40% in the 4-g food, 86.7% and 53.3% in the 6-g food, and 76.7% and 50% in the 8-g food. Weight of adult queen bee (1.459±0.191 g) and the number of ovarioles (41.7±21.3) were highest at 8 g of food. Results of this study are helpful for bee-keepers in producing fitter queen bees.

Sidelobe Reduction in Cognitive Radio Systems Using Hybrid Technique

Orthogonal frequency division multiplexing (OFDM) is one of the best candidates for dynamic spectrum access due to its flexibility of spectrum shaping. However, the high sidelobes of the OFDM signal that result in high out-of-band radiation, introduce significant interference to the users operating in its vicinity. This problem becomes more critical in cognitive radio (CR) system that enables the secondary users (SUs) users to access the spectrum holes not used by the primary users (PUs) at that time. In this paper, we present a generalized OFDM framework that has a capability of describing any sidelobe suppression techniques, despite of whether one or a number of techniques are used. Based on that framework, we propose cancellation carrier (CC) technique in conjunction with the generalized sidelobe canceller (GSC) to reduce the out-of-band radiation in the region where the licensed users are operating. Simulation results show that the proposed technique can reduce the out-of-band radiation better when compared with the existing techniques found in the literature.

Theoretical Investigation on the Dynamic Characteristics of One Degree of Freedom Vibration System Equipped with Inerter of Variable Inertance

In this paper, a theoretical investigation on the dynamic characteristics of one degree of freedom vibration system equipped with inerter of variable inertance, is presented. Differential equation of movement was solved under proper initial conditions in the case of free undamped/damped vibration, considered in the absence/presence of the inerter in the mechanical system. Influence of inertance on the amplitude of vibration, phase angle, natural frequency, damping ratio, and logarithmic decrement was clarified. It was mainly found that the inerter decreases the natural frequency of the undamped system and also of the damped system if the damping ratio is below 0.707. On the other hand, the inerter increases the natural frequency of the damped system if the damping ratio exceeds 0.707. Results obtained in this work are useful for the adequate design of inerters.

Productivity Effect of Urea Deep Placement Technology: An Empirical Analysis from Irrigation Rice Farmers in the Northern Region of Ghana

This study examined the effect of Urea Deep Placement (UDP) technology on the output of irrigated rice farmers in the northern region of Ghana. Multi-stage sampling technique was used to select 142 rice farmers from the Golinga and Bontanga irrigation schemes, around Tamale. A treatment effect model was estimated at two stages; firstly, to determine the factors that influenced farmers’ decision to adopt the UDP technology and secondly, to determine the effect of the adoption of the UDP technology on the output of rice farmers. The significant variables that influenced rice farmers’ adoption of the UPD technology were sex of the farmer, land ownership, off-farm activity, extension service, farmer group participation and training. The results also revealed that farm size and the adoption of UDP technology significantly influenced the output of rice farmers in the northern region of Ghana. In addition to the potential of the technology to improve yields, it also presents an employment opportunity for women and youth, who are engaged in the deep placement of Urea Super Granules (USG), as well as in the transplantation of rice. It is recommended that the government of Ghana work closely with the IFDC to embed the UDP technology in the national agricultural programmes and policies. The study also recommends an effective collaboration between the government, through the Ministry of Food and Agriculture (MoFA) and the International Fertilizer Development Center (IFDC) to train agricultural extension agents on UDP technology in the rice producing areas of the country.

Rail Corridors between Minimal Use of Train and Unsystematic Tightening of Population: A Methodological Essay

In the current situation, the automobile has become the main means of locomotion. It allows traveling long distances, encouraging urban sprawl. To counteract this trend, the train is often proposed as an alternative to the car. Simultaneously, the favoring of urban development around public transport nodes such as railway stations is one of the main issues of the coordination between urban planning and transportation and the keystone of the sustainable urban development implementation. In this context, this paper focuses on the study of the spatial structuring dynamics around the railway. Specifically, it is a question of studying the demographic dynamics in rail corridors of Nantes, Angers and Le Mans (Western France) basing on the radiation of railway stations. Consequently, the methodology is concentrated on the knowledge of demographic weight and gains of these corridors, the index of urban intensity and the mobility behaviors (workers’ travels, scholars' travels, modal practices of travels). The perimeter considered to define the rail corridors includes the communes of urban area which have a railway station and communes with an access time to the railway station is less than fifteen minutes by car (time specified by the Regional Transport Scheme of Travelers). The main tools used are the statistical data from the census of population, the basis of detailed tables and databases on mobility flows. The study reveals that the population is not tightened along rail corridors and train use is minimal despite the presence of a nearby railway station. These results lead to propose guidelines to make the train, a real vector of mobility across the rail corridors.

Adaptive Responses of Carum copticum to in vitro Salt Stress

Salinity is one of the most widespread agricultural problems in arid and semi-arid areas that limits the plant growth and crop productivity. In this study, the salt stress effects on protein, reducing sugar, proline contents and antioxidant enzymes activities of Carum copticum L. under in vitro conditions were studied. Seeds of C. copticum were cultured in Murashige and Skoog (MS) medium containing 0, 25, 50, 100 and 150 mM NaCl and calli were cultured in MS medium containing 1 μM 2, 4-dichlorophenoxyacetic acid, 4 μM benzyl amino purine and different levels of NaCl (0, 25, 50, 100 and 150 mM). After NaCl treatment for 28 days, the proline and reducing sugar contents of shoots, roots and calli increased significantly in relation to the severity of the salt stress. The highest amount of proline and carbohydrate were observed at 150 and 100 mM NaCl, respectively. The reducing sugar accumulation in shoots was the highest as compared to roots, whereas, proline contents did not show any significant difference in roots and shoots under salt stress. The results showed significant reduction of protein contents in seedlings and calli. Based on these results, proteins extracted from the shoots, roots and calli of C. copticum treated with 150 mM NaCl showed the lowest contents. The positive relationships were observed between activity of antioxidant enzymes and the increase in stress levels. Catalase, ascorbate peroxidase and superoxide dismutase activity increased significantly under salt concentrations in comparison to the control. These results suggest that the accumulation of proline and sugars, and activation of antioxidant enzymes play adaptive roles in the adaptation of seedlings and callus of C. copticum to saline conditions.

Thermodynamic Analyses of Information Dissipation along the Passive Dendritic Trees and Active Action Potential

Brain information transmission in the neuronal network occurs in the form of electrical signals. Neural work transmits information between the neurons or neurons and target cells by moving charged particles in a voltage field; a fraction of the energy utilized in this process is dissipated via entropy generation. Exergy loss and entropy generation models demonstrate the inefficiencies of the communication along the dendritic trees. In this study, neurons of 4 different animals were analyzed with one dimensional cable model with N=6 identical dendritic trees and M=3 order of symmetrical branching. Each branch symmetrically bifurcates in accordance with the 3/2 power law in an infinitely long cylinder with the usual core conductor assumptions, where membrane potential is conserved in the core conductor at all branching points. In the model, exergy loss and entropy generation rates are calculated for each branch of equivalent cylinders of electrotonic length (L) ranging from 0.1 to 1.5 for four different dendritic branches, input branch (BI), and sister branch (BS) and two cousin branches (BC-1 & BC-2). Thermodynamic analysis with the data coming from two different cat motoneuron studies show that in both experiments nearly the same amount of exergy is lost while generating nearly the same amount of entropy. Guinea pig vagal motoneuron loses twofold more exergy compared to the cat models and the squid exergy loss and entropy generation were nearly tenfold compared to the guinea pig vagal motoneuron model. Thermodynamic analysis show that the dissipated energy in the dendritic tress is directly proportional with the electrotonic length, exergy loss and entropy generation. Entropy generation and exergy loss show variability not only between the vertebrate and invertebrates but also within the same class. Concurrently, single action potential Na+ ion load, metabolic energy utilization and its thermodynamic aspect contributed for squid giant axon and mammalian motoneuron model. Energy demand is supplied to the neurons in the form of Adenosine triphosphate (ATP). Exergy destruction and entropy generation upon ATP hydrolysis are calculated. ATP utilization, exergy destruction and entropy generation showed differences in each model depending on the variations in the ion transport along the channels.

Optimal Tuning of Linear Quadratic Regulator Controller Using a Particle Swarm Optimization for Two-Rotor Aerodynamical System

This paper presents an optimal state feedback controller based on Linear Quadratic Regulator (LQR) for a two-rotor aero-dynamical system (TRAS). TRAS is a highly nonlinear multi-input multi-output (MIMO) system with two degrees of freedom and cross coupling. There are two parameters that define the behavior of LQR controller: state weighting matrix and control weighting matrix. The two parameters influence the performance of LQR. Particle Swarm Optimization (PSO) is proposed to optimally tune weighting matrices of LQR. The major concern of using LQR controller is to stabilize the TRAS by making the beam move quickly and accurately for tracking a trajectory or to reach a desired altitude. The simulation results were carried out in MATLAB/Simulink. The system is decoupled into two single-input single-output (SISO) systems. Comparing the performance of the optimized proportional, integral and derivative (PID) controller provided by INTECO, results depict that LQR controller gives a better performance in terms of both transient and steady state responses when PSO is performed.

Speeding up Nonlinear Time History Analysis of Base-Isolated Structures Using a Nonlinear Exponential Model

The nonlinear time history analysis of seismically base-isolated structures can require a significant computational effort when the behavior of each seismic isolator is predicted by adopting the widely used differential equation Bouc-Wen model. In this paper, a nonlinear exponential model, able to simulate the response of seismic isolation bearings within a relatively large displacements range, is described and adopted in order to reduce the numerical computations and speed up the nonlinear dynamic analysis. Compared to the Bouc-Wen model, the proposed one does not require the numerical solution of a nonlinear differential equation for each time step of the analysis. The seismic response of a 3d base-isolated structure with a lead rubber bearing system subjected to harmonic earthquake excitation is simulated by modeling each isolator using the proposed analytical model. The comparison of the numerical results and computational time with those obtained by modeling the lead rubber bearings using the Bouc-Wen model demonstrates the good accuracy of the proposed model and its capability to reduce significantly the computational effort of the analysis.

Mutation Analysis of the ATP7B Gene in 43 Vietnamese Wilson’s Disease Patients

Wilson’s disease (WD) is an autosomal recessive disorder of the copper metabolism, which is caused by a mutation in the copper-transporting P-type ATPase (ATP7B). The mechanism of this disease is the failure of hepatic excretion of copper to bile, and leads to copper deposits in the liver and other organs. The ATP7B gene is located on the long arm of chromosome 13 (13q14.3). This study aimed to investigate the gene mutation in the Vietnamese patients with WD, and make a presymptomatic diagnosis for their familial members. Forty-three WD patients and their 65 siblings were identified as having ATP7B gene mutations. Genomic DNA was extracted from peripheral blood samples; 21 exons and exon-intron boundaries of the ATP7B gene were analyzed by direct sequencing. We recognized four mutations ([R723=; H724Tfs*34], V1042Cfs*79, D1027H, and IVS6+3A>G) in the sum of 20 detectable mutations, accounting for 87.2% of the total. Mutation S105* was determined to have a high rate (32.6%) in this study. The hotspot regions of ATP7B were found at exons 2, 16, and 8, and intron 14, in 39.6 %, 11.6 %, 9.3%, and 7 % of patients, respectively. Among nine homozygote/compound heterozygote siblings of the patients with WD, three individuals were determined as asymptomatic by screening mutations of the probands. They would begin treatment after diagnosis. In conclusion, 20 different mutations were detected in 43 WD patients. Of this number, four novel mutations were explored, including [R723=; H724Tfs*34], V1042Cfs*79, D1027H, and IVS6+3A>G. The mutation S105* is the most prevalent and has been considered as a biomarker that can be used in a rapid detection assay for diagnosis of WD patients. Exons 2, 8, and 16, and intron 14 should be screened initially for WD patients in Vietnam. Based on risk profile for WD, genetic testing for presymptomatic patients is also useful in diagnosis and treatment.

The Role of Chemokine Family, CXCL-10 Urine as a Marker Diagnosis of Active Lung Tuberculosis in HIV/AIDS Patients

Human Immunodeficiency Virus (HIV) pandemic increased significantly worldwide. The rise in cases of HIV/AIDS was also followed by an increase in the incidence of opportunistic infection, with tuberculosis being the most opportunistic infection found in HIV/AIDS and the main cause of mortality in HIV/AIDS patients. Diagnosis of tuberculosis in HIV/AIDS patients is often difficult because of the uncommon symptom in HIV/AIDS patients compared to those without the disease. Thus, diagnostic tools are required that are more effective and efficient to diagnose tuberculosis in HIV/AIDS. CXCL-10/IP-10 is a chemokine that binds to the CXCR3 receptor found in HIV/AIDS patients with a weakened immune system. Tuberculosis infection in HIV/AIDS activates chemokine IP-10 in urine, which is used as a marker for diagnosis of infection. The aim of this study was to prove whether IP-10 urine can be a biomarker diagnosis of active lung tuberculosis in HIV-AIDS patients. Design of this study is a cross sectional study involving HIV/AIDS patients with lung tuberculosis as the subject of this study. Forty-seven HIV/AIDS patients with tuberculosis based on clinical and biochemical laboratory were asked to collect urine samples and IP-10/CXCL-10 urine being measured using ELISA method with 18 healthy human urine samples as control. Forty-seven patients diagnosed as HIV/AIDS were included as a subject of this study. HIV/AIDS were more common in male than in women with the percentage in male 85.1% vs. 14.5% of women. In this study, most diagnosed patients were aged 31-40 years old, followed by those 21-30 years, and > 40 years old, with one case diagnosed at age less than 20 years of age. From the result of the urine IP-10 using ELISA method, there was significant increase of the mean value of IP-10 urine in patients with TB-HIV/AIDS co-infection compared to the healthy control with mean 61.05 pg/mL ± 78.01 pg/mL vs. mean 17.2 pg/mL. Based on this research, there was significant increase of urine IP-10/CXCL-10 in active lung tuberculosis with HIV/AIDS compared to the healthy control. From this finding, it is necessary to conduct further research into whether urine IP-10/CXCL-10 plays a significant role in TB-HIV/AIDS co-infection, which can also be used as a biomarker in the early diagnosis of TB-HIV.

Effective Dose and Size Specific Dose Estimation with and without Tube Current Modulation for Thoracic Computed Tomography Examinations: A Phantom Study

The purpose of this study is to reduce radiation dose for chest CT examination by including Tube Current Modulation (TCM) to a standard CT protocol. A scan of an anthropomorphic male Alderson phantom was performed on a 128-slice scanner. The estimation of effective dose (ED) in both scans with and without mAs modulation was done via multiplication of Dose Length Product (DLP) to a conversion factor. Results were compared to those measured with a CT-Expo software. The size specific dose estimation (SSDE) values were obtained by multiplication of the volume CT dose index (CTDIvol) with a conversion size factor related to the phantom’s effective diameter. Objective assessment of image quality was performed with Signal to Noise Ratio (SNR) measurements in phantom. SPSS software was used for data analysis. Results showed including CARE Dose 4D; ED was lowered by 48.35% and 51.51% using DLP and CT-expo, respectively. In addition, ED ranges between 7.01 mSv and 6.6 mSv in case of standard protocol, while it ranges between 3.62 mSv and 3.2 mSv with TCM. Similar results are found for SSDE; dose was higher without TCM of 16.25 mGy and was lower by 48.8% including TCM. The SNR values calculated were significantly different (p=0.03

Probability-Based Damage Detection of Structures Using Model Updating with Enhanced Ideal Gas Molecular Movement Algorithm

Model updating method has received increasing attention in damage detection structures based on measured modal parameters. Therefore, a probability-based damage detection (PBDD) procedure based on a model updating procedure is presented in this paper, in which a one-stage model-based damage identification technique based on the dynamic features of a structure is investigated. The presented framework uses a finite element updating method with a Monte Carlo simulation that considers the uncertainty caused by measurement noise. Enhanced ideal gas molecular movement (EIGMM) is used as the main algorithm for model updating. Ideal gas molecular movement (IGMM) is a multiagent algorithm based on the ideal gas molecular movement. Ideal gas molecules disperse rapidly in different directions and cover all the space inside. This is embedded in the high speed of molecules, collisions between them and with the surrounding barriers. In IGMM algorithm to accomplish the optimal solutions, the initial population of gas molecules is randomly generated and the governing equations related to the velocity of gas molecules and collisions between those are utilized. In this paper, an enhanced version of IGMM, which removes unchanged variables after specified iterations, is developed. The proposed method is implemented on two numerical examples in the field of structural damage detection. The results show that the proposed method can perform well and competitive in PBDD of structures.

Nonlinear Dynamic Analysis of Base-Isolated Structures Using a Mixed Integration Method: Stability Aspects and Computational Efficiency

In order to reduce numerical computations in the nonlinear dynamic analysis of seismically base-isolated structures, a Mixed Explicit-Implicit time integration Method (MEIM) has been proposed. Adopting the explicit conditionally stable central difference method to compute the nonlinear response of the base isolation system, and the implicit unconditionally stable Newmark’s constant average acceleration method to determine the superstructure linear response, the proposed MEIM, which is conditionally stable due to the use of the central difference method, allows to avoid the iterative procedure generally required by conventional monolithic solution approaches within each time step of the analysis. The main aim of this paper is to investigate the stability and computational efficiency of the MEIM when employed to perform the nonlinear time history analysis of base-isolated structures with sliding bearings. Indeed, in this case, the critical time step could become smaller than the one used to define accurately the earthquake excitation due to the very high initial stiffness values of such devices. The numerical results obtained from nonlinear dynamic analyses of a base-isolated structure with a friction pendulum bearing system, performed by using the proposed MEIM, are compared to those obtained adopting a conventional monolithic solution approach, i.e. the implicit unconditionally stable Newmark’s constant acceleration method employed in conjunction with the iterative pseudo-force procedure. According to the numerical results, in the presented numerical application, the MEIM does not have stability problems being the critical time step larger than the ground acceleration one despite of the high initial stiffness of the friction pendulum bearings. In addition, compared to the conventional monolithic solution approach, the proposed algorithm preserves its computational efficiency even when it is adopted to perform the nonlinear dynamic analysis using a smaller time step.

An Advanced Exponential Model for Seismic Isolators Having Hardening or Softening Behavior at Large Displacements

In this paper, an advanced Nonlinear Exponential Model (NEM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement in the relatively large displacements range and a hardening or softening behavior at large displacements, is presented. The mathematical model is validated by comparing the experimental force-displacement hysteresis loops obtained during cyclic tests, conducted on a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted analytically. Good agreement between the experimental and simulated results shows that the proposed model can be an effective numerical tool to predict the force-displacement relationship of seismic isolation devices within the large displacements range. Compared to the widely used Bouc-Wen model, unable to simulate the response of seismic isolators at large displacements, the proposed one allows to avoid the numerical solution of a first order nonlinear ordinary differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort. Furthermore, the proposed model can simulate the smooth transition of the hysteresis loops from small to large displacements by adopting only one set of five parameters determined from the experimental hysteresis loops having the largest amplitude.

Influence of Displacement Amplitude and Vertical Load on the Horizontal Dynamic and Static Behavior of Helical Wire Rope Isolators

In this paper, the results of experimental tests performed on a Helical Wire Rope Isolator (HWRI) are presented in order to describe the dynamic and static behavior of the selected metal device in three different displacements ranges, namely small, relatively large, and large displacements ranges, without and under the effect of a vertical load. A testing machine, allowing to apply horizontal displacement or load histories to the tested bearing with a constant vertical load, has been adopted to perform the dynamic and static tests. According to the experimental results, the dynamic behavior of the tested device depends on the applied displacement amplitude. Indeed, the HWRI displays a softening and a hardening stiffness at small and relatively large displacements, respectively, and a stronger nonlinear stiffening behavior at large displacements. Furthermore, the experimental tests reveal that the application of a vertical load allows to have a more flexible device with higher damping properties and that the applied vertical load affects much less the dynamic response of the metal device at large displacements. Finally, a decrease in the static to dynamic effective stiffness ratio with increasing displacement amplitude has been observed.

Simulation of Dynamic Behavior of Seismic Isolators Using a Parallel Elasto-Plastic Model

In this paper, a one-dimensional (1d) Parallel Elasto- Plastic Model (PEPM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement, is presented. The parallel modeling concept is applied to discretize the continuously decreasing tangent stiffness function, thus allowing to simulate the dynamic behavior of seismic isolation bearings by putting linear elastic and nonlinear elastic-perfectly plastic elements in parallel. The mathematical model has been validated by comparing the experimental force-displacement hysteresis loops, obtained testing a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted numerically. Good agreement between the simulated and experimental results shows that the proposed model can be an effective numerical tool to predict the forcedisplacement relationship of seismic isolators within relatively large displacements. Compared to the widely used Bouc-Wen model, the proposed one allows to avoid the numerical solution of a first order ordinary nonlinear differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort, and requires the evaluation of only three model parameters from experimental tests, namely the initial tangent stiffness, the asymptotic tangent stiffness, and a parameter defining the transition from the initial to the asymptotic tangent stiffness.

Nonlinear Dynamic Analysis of Base-Isolated Structures Using a Partitioned Solution Approach and an Exponential Model

The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method.