Search results for: nonlinear calculation
1869 Dynamic Fault Diagnosis for Semi-Batch Reactor Under Closed-Loop Control via Independent RBFNN
Authors: Abdelkarim M. Ertiame, D. W. Yu, D. L. Yu, J. B. Gomm
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In this paper, a new robust fault detection and isolation (FDI) scheme is developed to monitor a multivariable nonlinear chemical process called the Chylla-Haase polymerization reactor when it is under the cascade PI control. The scheme employs a radial basis function neural network (RBFNN) in an independent mode to model the process dynamics and using the weighted sum-squared prediction error as the residual. The recursive orthogonal Least Squares algorithm (ROLS) is employed to train the model to overcome the training difficulty of the independent mode of the network. Then, another RBFNN is used as a fault classifier to isolate faults from different features involved in the residual vector. The several actuator and sensor faults are simulated in a nonlinear simulation of the reactor in Simulink. The scheme is used to detect and isolate the faults on-line. The simulation results show the effectiveness of the scheme even the process is subjected to disturbances and uncertainties including significant changes in the monomer feed rate, fouling factor, impurity factor, ambient temperature and measurement noise. The simulation results are presented to illustrate the effectiveness and robustness of the proposed method.Keywords: Robust fault detection, cascade control, independent RBF model, RBF neural networks, Chylla-Haase reactor, FDI under closed-loop control
Procedia PDF Downloads 4951868 A New Family of Integration Methods for Nonlinear Dynamic Analysis
Authors: Shuenn-Yih Chang, Chiu-LI Huang, Ngoc-Cuong Tran
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A new family of structure-dependent integration methods, whose coefficients of the difference equation for displacement increment are functions of the initial structural properties and the step size for time integration, is proposed in this work. This family method can simultaneously integrate the controllable numerical dissipation, explicit formulation and unconditional stability together. In general, its numerical dissipation can be continuously controlled by a parameter and it is possible to achieve zero damping. In addition, it can have high-frequency damping to suppress or even remove the spurious oscillations high frequency modes. Whereas, the low frequency modes can be very accurately integrated due to the almost zero damping for these low frequency modes. It is shown herein that the proposed family method can have exactly the same numerical properties as those of HHT-α method for linear elastic systems. In addition, it still preserves the most important property of a structure-dependent integration method, which is an explicit formulation for each time step. Consequently, it can save a huge computational efforts in solving inertial problems when compared to the HHT-α method. In fact, it is revealed by numerical experiments that the CPU time consumed by the proposed family method is only about 1.6% of that consumed by the HHT-α method for the 125-DOF system while it reduces to be 0.16% for the 1000-DOF system. Apparently, the saving of computational efforts is very significant.Keywords: structure-dependent integration method, nonlinear dynamic analysis, unconditional stability, numerical dissipation, accuracy
Procedia PDF Downloads 6371867 Insights Into Serotonin-Receptor Binding and Stability via Molecular Dynamics Simulations: Key Residues for Electrostatic Interactions and Signal Transduction
Authors: Arunima Verma, Padmabati Mondal
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Serotonin-receptor binding plays a key role in several neurological and biological processes, including mood, sleep, hunger, cognition, learning, and memory. In this article, we performed molecular dynamics simulation to examine the key residues that play an essential role in the binding of serotonin to the G-protein-coupled 5-HT₁ᴮ receptor (5-HT₁ᴮ R) via electrostatic interactions. An end-point free energy calculation method (MM-PBSA) determines the stability of the 5-HT1B R due to serotonin binding. The single-point mutation of the polar or charged amino acid residues (Asp129, Thr134) on the binding sites and the calculation of binding free energy validate the importance of these residues in the stability of the serotonin-receptor complex. Principal component analysis indicates the serotonin-bound 5-HT1BR is more stabilized than the apo-receptor in terms of dynamical changes. The difference dynamic cross-correlations map shows the correlation between the transmembrane and mini-Go, which indicates signal transduction happening between mini-Go and the receptor. Allosteric communication reveals the key nodes for signal transduction in 5-HT1BR. These results provide useful insights into the signal transduction pathways and mutagenesis study to regulate the functionality of the complex. The developed protocols can be applied to study local non-covalent interactions and long-range allosteric communications in any protein-ligand system for computer-aided drug design.Keywords: allostery, CADD, MD simulations, MM-PBSA
Procedia PDF Downloads 851866 Study of the Diaphragm Flexibility Effect on the Inelastic Seismic Response of Thin Wall Reinforced Concrete Buildings (TWRCB): A Purpose to Reduce the Uncertainty in the Vulnerability Estimation
Authors: A. Zapata, Orlando Arroyo, R. Bonett
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Over the last two decades, the growing demand for housing in Latin American countries has led to the development of construction projects based on low and medium-rise buildings with thin reinforced concrete walls. This system, known as Thin Walls Reinforced Concrete Buildings (TWRCB), uses walls with thicknesses from 100 to 150 millimetres, with flexural reinforcement formed by welded wire mesh (WWM) with diameters between 5 and 7 millimetres, arranged in one or two layers. These walls often have irregular structural configurations, including combinations of rectangular shapes. Experimental and numerical research conducted in regions where this structural system is commonplace indicates inherent weaknesses, such as limited ductility due to the WWM reinforcement and thin element dimensions. Because of its complexity, numerical analyses have relied on two-dimensional models that don't explicitly account for the floor system, even though it plays a crucial role in distributing seismic forces among the resilient elements. Nonetheless, the numerical analyses assume a rigid diaphragm hypothesis. For this purpose, two study cases of buildings were selected, low-rise and mid-rise characteristics of TWRCB in Colombia. The buildings were analyzed in Opensees using the MVLEM-3D for walls and shell elements to simulate the slabs to involve the effect of coupling diaphragm in the nonlinear behaviour. Three cases are considered: a) models without a slab, b) models with rigid slabs, and c) models with flexible slabs. An incremental static (pushover) and nonlinear dynamic analyses were carried out using a set of 44 far-field ground motions of the FEMA P-695, scaled to 1.0 and 1.5 factors to consider the probability of collapse for the design base earthquake (DBE) and the maximum considered earthquake (MCE) for the model, according to the location sites and hazard zone of the archetypes in the Colombian NSR-10. Shear base capacity, maximum displacement at the roof, walls shear base individual demands and probabilities of collapse were calculated, to evaluate the effect of absence, rigid and flexible slabs in the nonlinear behaviour of the archetype buildings. The pushover results show that the building exhibits an overstrength between 1.1 to 2 when the slab is considered explicitly and depends on the structural walls plan configuration; additionally, the nonlinear behaviour considering no slab is more conservative than if the slab is represented. Include the flexible slab in the analysis remarks the importance to consider the slab contribution in the shear forces distribution between structural elements according to design resistance and rigidity. The dynamic analysis revealed that including the slab reduces the collapse probability of this system due to have lower displacements and deformations, enhancing the safety of residents and the seismic performance. The strategy of including the slab in modelling is important to capture the real effect on the distribution shear forces in walls due to coupling to estimate the correct nonlinear behaviour in this system and the adequate distribution to proportionate the correct resistance and rigidity of the elements in the design to reduce the possibility of damage to the elements during an earthquake.Keywords: thin wall reinforced concrete buildings, coupling slab, rigid diaphragm, flexible diaphragm
Procedia PDF Downloads 721865 Iterative Estimator-Based Nonlinear Backstepping Control of a Robotic Exoskeleton
Authors: Brahmi Brahim, Mohammad Habibur Rahman, Maarouf Saad, Cristóbal Ochoa Luna
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A repetitive training movement is an efficient method to improve the ability and movement performance of stroke survivors and help them to recover their lost motor function and acquire new skills. The ETS-MARSE is seven degrees of freedom (DOF) exoskeleton robot developed to be worn on the lateral side of the right upper-extremity to assist and rehabilitate the patients with upper-extremity dysfunction resulting from stroke. Practically, rehabilitation activities are repetitive tasks, which make the assistive/robotic systems to suffer from repetitive/periodic uncertainties and external perturbations induced by the high-order dynamic model (seven DOF) and interaction with human muscle which impact on the tracking performance and even on the stability of the exoskeleton. To ensure the robustness and the stability of the robot, a new nonlinear backstepping control was implemented with designed tests performed by healthy subjects. In order to limit and to reject the periodic/repetitive disturbances, an iterative estimator was integrated into the control of the system. The estimator does not need the precise dynamic model of the exoskeleton. Experimental results confirm the robustness and accuracy of the controller performance to deal with the external perturbation, and the effectiveness of the iterative estimator to reject the repetitive/periodic disturbances.Keywords: backstepping control, iterative control, Rehabilitation, ETS-MARSE
Procedia PDF Downloads 2841864 Dissipation Capacity of Steel Building with Fiction Pendulum Base-Isolation System
Authors: A. Ras, I. Nait Zerrad, N. Benmouna, N. Boumechra
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Use of base isolators in the seismic design of structures has attracted considerable attention in recent years. The major concern in the design of these structures is to have enough lateral stability to resist wind and seismic forces. There are different systems providing such isolation, among them there are friction- pendulum base isolation systems (FPS) which are rather widely applied nowadays involving to both affordable cost and high fundamental periods. These devices are characterised by a stiff resistance against wind loads and to be flexible to the seismic tremors, which make them suitable for different situations. In this paper, a 3D numerical investigation is done considering the seismic response of a twelve-storey steel building retrofitted with a FPS. Fast nonlinear time history analysis (FNA) of Boumerdes earthquake (Algeria, May 2003) is considered for analysis and carried out using SAP2000 software. Comparisons between fixed base, bearing base isolated and braced structures are shown in a tabulated and graphical format. The results of the various alternatives studies to compare the structural response without and with this device of dissipation energy thus obtained were discussed and the conclusions showed the interesting potential of the FPS isolator. This system may to improve the dissipative capacities of the structure without increasing its rigidity in a significant way which contributes to optimize the quantity of steel necessary for its general stability.Keywords: energy dissipation, friction-pendulum system, nonlinear analysis, steel structure
Procedia PDF Downloads 2001863 Interaction Evaluation of Silver Ion and Silver Nanoparticles with Dithizone Complexes Using DFT Calculations and NMR Analysis
Authors: W. Nootcharin, S. Sujittra, K. Mayuso, K. Kornphimol, M. Rawiwan
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Silver has distinct antibacterial properties and has been used as a component of commercial products with many applications. An increasing number of commercial products cause risks of silver effects for human and environment such as the symptoms of Argyria and the release of silver to the environment. Therefore, the detection of silver in the aquatic environment is important. The colorimetric chemosensor is designed by the basic of ligand interactions with a metal ion, leading to the change of signals for the naked-eyes which are very useful method to this application. Dithizone ligand is considered as one of the effective chelating reagents for metal ions due to its high selectivity and sensitivity of a photochromic reaction for silver as well as the linear backbone of dithizone affords the rotation of various isomeric forms. The present study is focused on the conformation and interaction of silver ion and silver nanoparticles (AgNPs) with dithizone using density functional theory (DFT). The interaction parameters were determined in term of binding energy of complexes and the geometry optimization, frequency of the structures and calculation of binding energies using density functional approaches B3LYP and the 6-31G(d,p) basis set. Moreover, the interaction of silver–dithizone complexes was supported by UV–Vis spectroscopy, FT-IR spectrum that was simulated by using B3LYP/6-31G(d,p) and 1H NMR spectra calculation using B3LYP/6-311+G(2d,p) method compared with the experimental data. The results showed the ion exchange interaction between hydrogen of dithizone and silver atom, with minimized binding energies of silver–dithizone interaction. However, the result of AgNPs in the form of complexes with dithizone. Moreover, the AgNPs-dithizone complexes were confirmed by using transmission electron microscope (TEM). Therefore, the results can be the useful information for determination of complex interaction using the analysis of computer simulations.Keywords: silver nanoparticles, dithizone, DFT, NMR
Procedia PDF Downloads 2071862 The Influence of Shear Wall Position on Seismic Performance in Buildings
Authors: Akram Khelaifia, Nesreddine Djafar Henni
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Reinforced concrete shear walls are essential components in protecting buildings from seismic forces by providing both strength and stiffness. This study focuses on optimizing the placement of shear walls in a high seismic zone. Through nonlinear analyses conducted on an eight-story building, various scenarios of shear wall positions are investigated to evaluate their impact on seismic performance. Employing a performance-based seismic design (PBSD) approach, the study aims to meet acceptance criteria related to inter-story drift ratio and damage levels. The findings emphasize the importance of concentrating shear walls in the central area of the building during the design phase. This strategic placement proves more effective compared to peripheral distributions, resulting in reduced inter-story drift and mitigated potential damage during seismic events. Additionally, the research explores the use of shear walls that completely infill the frame, forming compound shapes like Box configurations. It is discovered that incorporating such complete shear walls significantly enhances the structure's reliability concerning inter-story drift. Conversely, the absence of complete shear walls within the frame leads to reduced stiffness and the potential deterioration of short beams.Keywords: performance level, pushover analysis, shear wall, plastic hinge, nonlinear analyses
Procedia PDF Downloads 511861 Analysis of Nonlinear Dynamic Systems Excited by Combined Colored and White Noise Excitations
Authors: Siu-Siu Guo, Qingxuan Shi
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In this paper, single-degree-of-freedom (SDOF) systems to white noise and colored noise excitations are investigated. By expressing colored noise excitation as a second-order filtered white noise process and introducing colored noise as an additional state variable, the equation of motion for SDOF system under colored noise is then transferred artificially to multi-degree-of-freedom (MDOF) system under white noise excitations. As a consequence, corresponding Fokker-Planck-Kolmogorov (FPK) equation governing the joint probabilistic density function (PDF) of state variables increases to 4-dimension (4-D). Solution procedure and computer programme become much more sophisticated. The exponential-polynomial closure (EPC) method, widely applied for cases of SDOF systems under white noise excitations, is developed and improved for cases of systems under colored noise excitations and for solving the complex 4-D FPK equation. On the other hand, Monte Carlo simulation (MCS) method is performed to test the approximate EPC solutions. Two examples associated with Gaussian and non-Gaussian colored noise excitations are considered. Corresponding band-limited power spectral densities (PSDs) for colored noise excitations are separately given. Numerical studies show that the developed EPC method provides relatively accurate estimates of the stationary probabilistic solutions. Moreover, statistical parameter of mean-up crossing rate (MCR) is taken into account, which is important for reliability and failure analysis.Keywords: filtered noise, narrow-banded noise, nonlinear dynamic, random vibration
Procedia PDF Downloads 2241860 Improving the Global Competitiveness of SMEs by Logistics Transportation Management: Case Study Chicken Meat Supply Chain
Authors: P. Vanichkobchinda
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The Logistics Transportation techniques, Open Vehicle Routing (OVR) is an approach toward transportation cost reduction, especially for long distance pickup and delivery nodes. The outstanding characteristic of OVR is that the route starting node and ending node are not necessary the same as in typical vehicle routing problems. This advantage enables the routing to flow continuously and the vehicle does not always return to its home base. This research aims to develop a heuristic for the open vehicle routing problem with pickup and delivery under time window and loading capacity constraints to minimize the total distance. The proposed heuristic is developed based on the Insertion method, which is a simple method and suitable for the rapid calculation that allows insertion of the new additional transportation requirements along the original paths. According to the heuristic analysis, cost comparisons between the proposed heuristic and companies are using method, nearest neighbor method show that the insertion heuristic. Moreover, the proposed heuristic gave superior solutions in all types of test problems. In conclusion, the proposed heuristic can effectively and efficiently solve the open vehicle routing. The research indicates that the improvement of new transport's calculation and the open vehicle routing with "Insertion Heuristic" represent a better outcome with 34.3 percent in average. in cost savings. Moreover, the proposed heuristic gave superior solutions in all types of test problems. In conclusion, the proposed heuristic can effectively and efficiently solve the open vehicle routing.Keywords: business competitiveness, cost reduction, SMEs, logistics transportation, VRP
Procedia PDF Downloads 6831859 The Effect of Soil-Structure Interaction on the Post-Earthquake Fire Performance of Structures
Authors: A. T. Al-Isawi, P. E. F. Collins
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The behaviour of structures exposed to fire after an earthquake is not a new area of engineering research, but there remain a number of areas where further work is required. Such areas relate to the way in which seismic excitation is applied to a structure, taking into account the effect of soil-structure interaction (SSI) and the method of analysis, in addition to identifying the excitation load properties. The selection of earthquake data input for use in nonlinear analysis and the method of analysis are still challenging issues. Thus, realistic artificial ground motion input data must be developed to certify that site properties parameters adequately describe the effects of the nonlinear inelastic behaviour of the system and that the characteristics of these parameters are coherent with the characteristics of the target parameters. Conversely, ignoring the significance of some attributes, such as frequency content, soil site properties and earthquake parameters may lead to misleading results, due to the misinterpretation of required input data and the incorrect synthesise of analysis hypothesis. This paper presents a study of the post-earthquake fire (PEF) performance of a multi-storey steel-framed building resting on soft clay, taking into account the effects of the nonlinear inelastic behaviour of the structure and soil, and the soil-structure interaction (SSI). Structures subjected to an earthquake may experience various levels of damage; the geometrical damage, which indicates the change in the initial structure’s geometry due to the residual deformation as a result of plastic behaviour, and the mechanical damage which identifies the degradation of the mechanical properties of the structural elements involved in the plastic range of deformation. Consequently, the structure presumably experiences partial structural damage but is then exposed to fire under its new residual material properties, which may result in building failure caused by a decrease in fire resistance. This scenario would be more complicated if SSI was also considered. Indeed, most earthquake design codes ignore the probability of PEF as well as the effect that SSI has on the behaviour of structures, in order to simplify the analysis procedure. Therefore, the design of structures based on existing codes which neglect the importance of PEF and SSI can create a significant risk of structural failure. In order to examine the criteria for the behaviour of a structure under PEF conditions, a two-dimensional nonlinear elasto-plastic model is developed using ABAQUS software; the effects of SSI are included. Both geometrical and mechanical damages have been taken into account after the earthquake analysis step. For comparison, an identical model is also created, which does not include the effects of soil-structure interaction. It is shown that damage to structural elements is underestimated if SSI is not included in the analysis, and the maximum percentage reduction in fire resistance is detected in the case when SSI is included in the scenario. The results are validated using the literature.Keywords: Abaqus Software, Finite Element Analysis, post-earthquake fire, seismic analysis, soil-structure interaction
Procedia PDF Downloads 1201858 Dynamics of Mach Zehnder Modulator in Open and Closed Loop Bias Condition
Authors: Ramonika Sengupta, Stuti Kachhwaha, Asha Adhiya, K. Satya Raja Sekhar, Rajwinder Kaur
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Numerous efforts have been done in the past decade to develop the methods of secure communication that are free from interception and eavesdropping. In fiber optic communication, chaotic optical carrier signals are used for data encryption in secure data transmission. Mach-Zehnder Modulators (MZM) are the key components for generating the chaotic signals to be used as optical carriers. This paper presents the dynamics of a lithium niobate MZM modulator under various biasing conditions. The chaotic fluctuations of the intensity of a laser diode have been generated using the electro-optic MZM modulator operating in a highly nonlinear regime. The modulator is driven in closed loop by its own output at an earlier time. When used as an electro-optic oscillator employing delayed feedback, the MZM displays a wide range of output waveforms of varying complexity. The dynamical behavior of the system ranges from periodic to nonlinear oscillations. The nonlinearity displayed by the system is reproducible and is easily controllable. In this paper, we demonstrate a wide variety of optical signals generated by MZM using easily controllable device parameters in both open and close loop bias conditions.Keywords: chaotic carrier, fiber optic communication, Mach-Zehnder modulator, secure data transmission
Procedia PDF Downloads 2711857 Regularized Euler Equations for Incompressible Two-Phase Flow Simulations
Authors: Teng Li, Kamran Mohseni
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This paper presents an inviscid regularization technique for the incompressible two-phase flow simulations. This technique is known as observable method due to the understanding of observability that any feature smaller than the actual resolution (physical or numerical), i.e., the size of wire in hotwire anemometry or the grid size in numerical simulations, is not able to be captured or observed. Differ from most regularization techniques that applies on the numerical discretization, the observable method is employed at PDE level during the derivation of equations. Difficulties in the simulation and analysis of realistic fluid flow often result from discontinuities (or near-discontinuities) in the calculated fluid properties or state. Accurately capturing these discontinuities is especially crucial when simulating flows involving shocks, turbulence or sharp interfaces. Over the past several years, the properties of this new regularization technique have been investigated that show the capability of simultaneously regularizing shocks and turbulence. The observable method has been performed on the direct numerical simulations of shocks and turbulence where the discontinuities are successfully regularized and flow features are well captured. In the current paper, the observable method will be extended to two-phase interfacial flows. Multiphase flows share the similar features with shocks and turbulence that is the nonlinear irregularity caused by the nonlinear terms in the governing equations, namely, Euler equations. In the direct numerical simulation of two-phase flows, the interfaces are usually treated as the smooth transition of the properties from one fluid phase to the other. However, in high Reynolds number or low viscosity flows, the nonlinear terms will generate smaller scales which will sharpen the interface, causing discontinuities. Many numerical methods for two-phase flows fail at high Reynolds number case while some others depend on the numerical diffusion from spatial discretization. The observable method regularizes this nonlinear mechanism by filtering the convective terms and this process is inviscid. The filtering effect is controlled by an observable scale which is usually about a grid length. Single rising bubble and Rayleigh-Taylor instability are studied, in particular, to examine the performance of the observable method. A pseudo-spectral method is used for spatial discretization which will not introduce numerical diffusion, and a Total Variation Diminishing (TVD) Runge Kutta method is applied for time integration. The observable incompressible Euler equations are solved for these two problems. In rising bubble problem, the terminal velocity and shape of the bubble are particularly examined and compared with experiments and other numerical results. In the Rayleigh-Taylor instability, the shape of the interface are studied for different observable scale and the spike and bubble velocities, as well as positions (under a proper observable scale), are compared with other simulation results. The results indicate that this regularization technique can potentially regularize the sharp interface in the two-phase flow simulationsKeywords: Euler equations, incompressible flow simulation, inviscid regularization technique, two-phase flow
Procedia PDF Downloads 4981856 Classification of ECG Signal Based on Mixture of Linear and Non-Linear Features
Authors: Mohammad Karimi Moridani, Mohammad Abdi Zadeh, Zahra Shahiazar Mazraeh
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In recent years, the use of intelligent systems in biomedical engineering has increased dramatically, especially in the diagnosis of various diseases. Also, due to the relatively simple recording of the electrocardiogram signal (ECG), this signal is a good tool to show the function of the heart and diseases associated with it. The aim of this paper is to design an intelligent system for automatically detecting a normal electrocardiogram signal from abnormal one. Using this diagnostic system, it is possible to identify a person's heart condition in a very short time and with high accuracy. The data used in this article are from the Physionet database, available in 2016 for use by researchers to provide the best method for detecting normal signals from abnormalities. Data is of both genders and the data recording time varies between several seconds to several minutes. All data is also labeled normal or abnormal. Due to the low positional accuracy and ECG signal time limit and the similarity of the signal in some diseases with the normal signal, the heart rate variability (HRV) signal was used. Measuring and analyzing the heart rate variability with time to evaluate the activity of the heart and differentiating different types of heart failure from one another is of interest to the experts. In the preprocessing stage, after noise cancelation by the adaptive Kalman filter and extracting the R wave by the Pan and Tampkinz algorithm, R-R intervals were extracted and the HRV signal was generated. In the process of processing this paper, a new idea was presented that, in addition to using the statistical characteristics of the signal to create a return map and extraction of nonlinear characteristics of the HRV signal due to the nonlinear nature of the signal. Finally, the artificial neural networks widely used in the field of ECG signal processing as well as distinctive features were used to classify the normal signals from abnormal ones. To evaluate the efficiency of proposed classifiers in this paper, the area under curve ROC was used. The results of the simulation in the MATLAB environment showed that the AUC of the MLP and SVM neural network was 0.893 and 0.947, respectively. As well as, the results of the proposed algorithm in this paper indicated that the more use of nonlinear characteristics in normal signal classification of the patient showed better performance. Today, research is aimed at quantitatively analyzing the linear and non-linear or descriptive and random nature of the heart rate variability signal, because it has been shown that the amount of these properties can be used to indicate the health status of the individual's heart. The study of nonlinear behavior and dynamics of the heart's neural control system in the short and long-term provides new information on how the cardiovascular system functions, and has led to the development of research in this field. Given that the ECG signal contains important information and is one of the common tools used by physicians to diagnose heart disease, but due to the limited accuracy of time and the fact that some information about this signal is hidden from the viewpoint of physicians, the design of the intelligent system proposed in this paper can help physicians with greater speed and accuracy in the diagnosis of normal and patient individuals and can be used as a complementary system in the treatment centers.Keywords: neart rate variability, signal processing, linear and non-linear features, classification methods, ROC Curve
Procedia PDF Downloads 2621855 Numerical Solution of Space Fractional Order Linear/Nonlinear Reaction-Advection Diffusion Equation Using Jacobi Polynomial
Authors: Shubham Jaiswal
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During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.Keywords: space fractional order linear/nonlinear reaction-advection diffusion equation, shifted Jacobi polynomials, operational matrix, collocation method, Caputo derivative
Procedia PDF Downloads 4431854 Study on the Process of Detumbling Space Target by Laser
Authors: Zhang Pinliang, Chen Chuan, Song Guangming, Wu Qiang, Gong Zizheng, Li Ming
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The active removal of space debris and asteroid defense are important issues in human space activities. Both of them need a detumbling process, for almost all space debris and asteroid are in a rotating state, and it`s hard and dangerous to capture or remove a target with a relatively high tumbling rate. So it`s necessary to find a method to reduce the angular rate first. The laser ablation method is an efficient way to tackle this detumbling problem, for it`s a contactless technique and can work at a safe distance. In existing research, a laser rotational control strategy based on the estimation of the instantaneous angular velocity of the target has been presented. But their calculation of control torque produced by a laser, which is very important in detumbling operation, is not accurate enough, for the method they used is only suitable for the plane or regularly shaped target, and they did not consider the influence of irregular shape and the size of the spot. In this paper, based on the triangulation reconstruction of the target surface, we propose a new method to calculate the impulse of the irregularly shaped target under both the covered irradiation and spot irradiation of the laser and verify its accuracy by theoretical formula calculation and impulse measurement experiment. Then we use it to study the process of detumbling cylinder and asteroid by laser. The result shows that the new method is universally practical and has high precision; it will take more than 13.9 hours to stop the rotation of Bennu with 1E+05kJ laser pulse energy; the speed of the detumbling process depends on the distance between the spot and the centroid of the target, which can be found an optimal value in every particular case.Keywords: detumbling, laser ablation drive, space target, space debris remove
Procedia PDF Downloads 821853 Modeling of Sediment Yield and Streamflow of Watershed Basin in the Philippines Using the Soil Water Assessment Tool Model for Watershed Sustainability
Authors: Warda L. Panondi, Norihiro Izumi
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Sedimentation is a significant threat to the sustainability of reservoirs and their watershed. In the Philippines, the Pulangi watershed experienced a high sediment loss mainly due to land conversions and plantations that showed critical erosion rates beyond the tolerable limit of -10 ton/ha/yr in all of its sub-basin. From this event, the prediction of runoff volume and sediment yield is essential to examine using the country's soil conservation techniques realistically. In this research, the Pulangi watershed was modeled using the soil water assessment tool (SWAT) to predict its watershed basin's annual runoff and sediment yield. For the calibration and validation of the model, the SWAT-CUP was utilized. The model was calibrated with monthly discharge data for 1990-1993 and validated for 1994-1997. Simultaneously, the sediment yield was calibrated in 2014 and validated in 2015 because of limited observed datasets. Uncertainty analysis and calculation of efficiency indexes were accomplished through the SUFI-2 algorithm. According to the coefficient of determination (R2), Nash Sutcliffe efficiency (NSE), King-Gupta efficiency (KGE), and PBIAS, the calculation of streamflow indicates a good performance for both calibration and validation periods while the sediment yield resulted in a satisfactory performance for both calibration and validation. Therefore, this study was able to identify the most critical sub-basin and severe needs of soil conservation. Furthermore, this study will provide baseline information to prevent floods and landslides and serve as a useful reference for land-use policies and watershed management and sustainability in the Pulangi watershed.Keywords: Pulangi watershed, sediment yield, streamflow, SWAT model
Procedia PDF Downloads 2071852 [Keynote Talk]: Applying p-Balanced Energy Technique to Solve Liouville-Type Problems in Calculus
Authors: Lina Wu, Ye Li, Jia Liu
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We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in Lq space to infinite in non-Lq space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.Keywords: differential forms, holder inequality, Liouville-type problems, p-balanced growth, p-harmonic maps, q-energy growth, tests for series
Procedia PDF Downloads 2331851 Constructions of Linear and Robust Codes Based on Wavelet Decompositions
Authors: Alla Levina, Sergey Taranov
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The classical approach to the providing noise immunity and integrity of information that process in computing devices and communication channels is to use linear codes. Linear codes have fast and efficient algorithms of encoding and decoding information, but this codes concentrate their detect and correct abilities in certain error configurations. To protect against any configuration of errors at predetermined probability can robust codes. This is accomplished by the use of perfect nonlinear and almost perfect nonlinear functions to calculate the code redundancy. The paper presents the error-correcting coding scheme using biorthogonal wavelet transform. Wavelet transform applied in various fields of science. Some of the wavelet applications are cleaning of signal from noise, data compression, spectral analysis of the signal components. The article suggests methods for constructing linear codes based on wavelet decomposition. For developed constructions we build generator and check matrix that contain the scaling function coefficients of wavelet. Based on linear wavelet codes we develop robust codes that provide uniform protection against all errors. In article we propose two constructions of robust code. The first class of robust code is based on multiplicative inverse in finite field. In the second robust code construction the redundancy part is a cube of information part. Also, this paper investigates the characteristics of proposed robust and linear codes.Keywords: robust code, linear code, wavelet decomposition, scaling function, error masking probability
Procedia PDF Downloads 4881850 Research the Causes of Defects and Injuries of Reinforced Concrete and Stone Construction
Authors: Akaki Qatamidze
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Implementation of the project will be a step forward in terms of reliability in Georgia and the improvement of the construction and the development of construction. Completion of the project is expected to result in a complete knowledge, which is expressed in concrete and stone structures of assessing the technical condition of the processing. This method is based on a detailed examination of the structure, in order to establish the injuries and the elimination of the possibility of changing the structural scheme of the new requirements and architectural preservationists. Reinforced concrete and stone structures research project carried out in a systematic analysis of the important approach is to optimize the process of research and development of new knowledge in the neighboring areas. In addition, the problem of physical and mathematical models of rational consent, the main pillar of the physical (in-situ) data and mathematical calculation models and physical experiments are used only for the calculation model specification and verification. Reinforced concrete and stone construction defects and failures the causes of the proposed research to enhance the effectiveness of their maximum automation capabilities and expenditure of resources to reduce the recommended system analysis of the methodological concept-based approach, as modern science and technology major particularity of one, it will allow all family structures to be identified for the same work stages and procedures, which makes it possible to exclude subjectivity and addresses the problem of the optimal direction. It discussed the methodology of the project and to establish a major step forward in the construction trades and practical assistance to engineers, supervisors, and technical experts in the construction of the settlement of the problem.Keywords: building, reinforced concrete, expertise, stone structures
Procedia PDF Downloads 3351849 Automation of Embodied Energy Calculations for Buildings through Building Information Modelling
Authors: Ahmad Odeh
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Researchers are currently more concerned about the calculations of energy at the operational stage, mainly due to its larger environmental impact, but the fact remains, embodied energies represent a substantial contributor unaccounted for in the overall energy computation method. The calculation of materials’ embodied energy during the construction stage is complicated. This is due to the various factors involved. The equipment used, fuel needed, and electricity required for each type of materials varies with location and thus the embodied energy will differ for each project. Moreover, the method used in manufacturing, transporting and putting in place will have significant influence on the materials’ embodied energy. This anomaly has made it difficult to calculate or even bench mark the usage of such energies. This paper presents a model aimed at calculating embodied energies based on such variabilities. It presents a systematic approach that uses an efficient method of calculation to provide a new insight for the selection of construction materials. The model is developed in a BIM environment. The quantification of materials’ energy is determined over the three main stages of their lifecycle: manufacturing, transporting and placing. The model uses three major databases each of which contains set of the construction materials that are most commonly used in building projects. The first dataset holds information about the energy required to manufacture any type of materials, the second includes information about the energy required for transporting the materials while the third stores information about the energy required by machinery to place the materials in their intended locations. Through geospatial data analysis, the model automatically calculates the distances between the suppliers and construction sites and then uses dataset information for energy computations. The computational sum of all the energies is automatically calculated and then the model provides designers with a list of usable equipment along with the associated embodied energies.Keywords: BIM, lifecycle energy assessment, building automation, energy conservation
Procedia PDF Downloads 1881848 An Adiabatic Quantum Optimization Approach for the Mixed Integer Nonlinear Programming Problem
Authors: Maxwell Henderson, Tristan Cook, Justin Chan Jin Le, Mark Hodson, YoungJung Chang, John Novak, Daniel Padilha, Nishan Kulatilaka, Ansu Bagchi, Sanjoy Ray, John Kelly
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We present a method of using adiabatic quantum optimization (AQO) to solve a mixed integer nonlinear programming (MINLP) problem instance. The MINLP problem is a general form of a set of NP-hard optimization problems that are critical to many business applications. It requires optimizing a set of discrete and continuous variables with nonlinear and potentially nonconvex constraints. Obtaining an exact, optimal solution for MINLP problem instances of non-trivial size using classical computation methods is currently intractable. Current leading algorithms leverage heuristic and divide-and-conquer methods to determine approximate solutions. Creating more accurate and efficient algorithms is an active area of research. Quantum computing (QC) has several theoretical benefits compared to classical computing, through which QC algorithms could obtain MINLP solutions that are superior to current algorithms. AQO is a particular form of QC that could offer more near-term benefits compared to other forms of QC, as hardware development is in a more mature state and devices are currently commercially available from D-Wave Systems Inc. It is also designed for optimization problems: it uses an effect called quantum tunneling to explore all lowest points of an energy landscape where classical approaches could become stuck in local minima. Our work used a novel algorithm formulated for AQO to solve a special type of MINLP problem. The research focused on determining: 1) if the problem is possible to solve using AQO, 2) if it can be solved by current hardware, 3) what the currently achievable performance is, 4) what the performance will be on projected future hardware, and 5) when AQO is likely to provide a benefit over classical computing methods. Two different methods, integer range and 1-hot encoding, were investigated for transforming the MINLP problem instance constraints into a mathematical structure that can be embedded directly onto the current D-Wave architecture. For testing and validation a D-Wave 2X device was used, as well as QxBranch’s QxLib software library, which includes a QC simulator based on simulated annealing. Our results indicate that it is mathematically possible to formulate the MINLP problem for AQO, but that currently available hardware is unable to solve problems of useful size. Classical general-purpose simulated annealing is currently able to solve larger problem sizes, but does not scale well and such methods would likely be outperformed in the future by improved AQO hardware with higher qubit connectivity and lower temperatures. If larger AQO devices are able to show improvements that trend in this direction, commercially viable solutions to the MINLP for particular applications could be implemented on hardware projected to be available in 5-10 years. Continued investigation into optimal AQO hardware architectures and novel methods for embedding MINLP problem constraints on to those architectures is needed to realize those commercial benefits.Keywords: adiabatic quantum optimization, mixed integer nonlinear programming, quantum computing, NP-hard
Procedia PDF Downloads 5241847 Correlation Between Diastolic Function and Lower GLS in Hypertensive Patients
Authors: A. Kherraf, S. Ouarrak, L. Azzouzi, R. Habbal
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Introduction: Preserved LVEF heart failure is an important cause of mortality and morbidity in hypertensive patients. A strong correlation between impaired diastolic function and longitudinal systolic dysfunction. could have several explanations, first, the diastole is an energy dependent process, especially during its first phase, it also includes active systolic components during the phase of iso volumetric relaxation, in addition, the impairment of the intrinsic myocytic function is part of hypertensive pathology as evidenced by recent studies. METHODS AND MATERIALS: This work consists of performing in a series of 333 hypertensive patients (aged 25 to 75 years) a complete echocardiographic study, including LVEF by Simpson biplane method, the calculation of the indexed left ventricular mass, the analysis of the diastolic function, and finally, the study of the longitudinal deformation of the LV by the technique of speckletracking (calculation of the GLS). Patients with secondary hypertension, leaky or stenosing valve disease, arrhythmia, and a history of coronary insufficiency were excluded from this study. RESULTS: Of the 333 hypertensive patients, 225 patients (67.5%) had impaired diastolic function, of which 60 patients (18%) had high filling pressures. 49.39% had echocardigraphic HVG, Almost all of these patients (60 patients) had low GLS. There is a statistically very significant relationship between lower GLS and increased left ventricular filling pressures in hypertensive patients. These results suggest that increased filling pressures are closely associated with atrioventricular interaction in patients with hypertension, with a strong correlation with impairment of longitudinal systolic function and diastolic function CONCLUSION: Overall, a linear relationship is established between increased left ventricular mass, diastolic dysfunction, and longitudinal LV systolic dysfunctionKeywords: hypertension, diastolic function, left ventricle, heart failure
Procedia PDF Downloads 1251846 Analysis of Force Convection in Bandung Triga Reactor Core Plate Types Fueled Using Coolod-N2
Authors: K. A. Sudjatmi, Endiah Puji Hastuti, Surip Widodo, Reinaldy Nazar
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Any pretensions to stop the production of TRIGA fuel elements by TRIGA reactor fuel elements manufacturer should be anticipated by the operating agency of TRIGA reactor to replace the cylinder type fuel element with plate type fuel element, that available on the market. This away was performed the calculation on U3Si2Al fuel with uranium enrichment of 19.75% and a load level of 2.96 gU/cm3. Maximum power that can be operated on free convection cooling mode at the BANDUNG TRIGA reactor fuel plate was 600 kW. This study has been conducted thermalhydraulic characteristic calculation model of the reactor core power 2MW. BANDUNG TRIGA reactor core fueled plate type is composed of 16 fuel elements, 4 control elements and one irradiation facility which is located right in the middle of the core. The reactor core is cooled using a pump which is already available with flow rate 900 gpm. Analysis on forced convection cooling mode with flow from the top down from 10%, 20%, 30% and so on up to a 100% rate of coolant flow. performed using the COOLOD-N2 code. The calculations result showed that the 2 MW power with inlet coolant temperature at 37 °C and cooling rate percentage of 50%, then the coolant temperature, maximum cladding and meat respectively 64.96 oC, 124.81 oC, and 125.08 oC, DNBR (departure from nucleate boiling ratio)=1.23 and OFIR (onset of flow instability ratio)=1:00. The results are expected to be used as a reference for determining the power and cooling rate level of the BANDUNG TRIGA reactor core plate types fueled.Keywords: TRIGA, COOLOD-N2, plate type fuel element, force convection, thermal hydraulic characteristic
Procedia PDF Downloads 2981845 A Broadband Tri-Cantilever Vibration Energy Harvester with Magnetic Oscillator
Authors: Xiaobo Rui, Zhoumo Zeng, Yibo Li
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A novel tri-cantilever energy harvester with magnetic oscillator was presented, which could convert the ambient vibration into electrical energy to power the low-power devices such as wireless sensor networks. The most common way to harvest vibration energy is based on the use of linear resonant devices such as cantilever beam, since this structure creates the highest strain for a given force. The highest efficiency will be achieved when the resonance frequency of the harvester matches the vibration frequency. The limitation of the structure is the narrow effective bandwidth. To overcome this limitation, this article introduces a broadband tri-cantilever harvester with nonlinear stiffness. This energy harvester typically consists of three thin cantilever beams vertically arranged with Neodymium Magnets ( NdFeB)magnetics at its free end and a fixed base at the other end. The three cantilevers have different resonant frequencies by designed in different thicknesses. It is obviously that a similar advantage of multiple resonant frequencies as piezoelectric cantilevers array structure is built. To achieve broadband energy harvesting, magnetic interaction is used to introduce the nonlinear system stiffness to tune the resonant frequency to match the excitation. Since the three cantilever tips are all free and the magnetic force is distance dependent, the resonant frequencies will be complexly changed with the vertical vibration of the free end. Both model and experiment are built. The electromechanically coupled lumped-parameter model is presented. An electromechanical formulation and analytical expressions for the coupled nonlinear vibration response and voltage response are given. The entire structure is fabricated and mechanically attached to a electromagnetic shaker as a vibrating body via the fixed base, in order to couple the vibrations to the cantilever. The cantilevers are bonded with piezoelectric macro-fiber composite (MFC) materials (Model: M8514P2). The size of the cantilevers is 120*20mm2 and the thicknesses are separately 1mm, 0.8mm, 0.6mm. The prototype generator has a measured performance of 160.98 mW effective electrical power and 7.93 DC output voltage via the excitation level of 10m/s2. The 130% increase in the operating bandwidth is achieved. This device is promising to support low-power devices, peer-to-peer wireless nodes, and small-scale wireless sensor networks in ambient vibration environment.Keywords: tri-cantilever, ambient vibration, energy harvesting, magnetic oscillator
Procedia PDF Downloads 1541844 Extreme Value Theory Applied in Reliability Analysis: Case Study of Diesel Generator Fans
Authors: Jelena Vucicevic
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Reliability analysis represents a very important task in different areas of work. In any industry, this is crucial for maintenance, efficiency, safety and monetary costs. There are ways to calculate reliability, unreliability, failure density and failure rate. In this paper, the results for the reliability of diesel generator fans were calculated through Extreme Value Theory. The Extreme Value Theory is not widely used in the engineering field. Its usage is well known in other areas such as hydrology, meteorology, finance. The significance of this theory is in the fact that unlike the other statistical methods it is focused on rare and extreme values, and not on average. It should be noted that this theory is not designed exclusively for extreme events, but for extreme values in any event. Therefore, this is a great opportunity to apply the theory and test if it could be applied in this situation. The significance of the work is the calculation of time to failure or reliability in a new way, using statistic. Another advantage of this calculation is that there is no need for technical details and it can be implemented in any part for which we need to know the time to fail in order to have appropriate maintenance, but also to maximize usage and minimize costs. In this case, calculations have been made on diesel generator fans but the same principle can be applied to any other part. The data for this paper came from a field engineering study of the time to failure of diesel generator fans. The ultimate goal was to decide whether or not to replace the working fans with a higher quality fan to prevent future failures. The results achieved in this method will show the approximation of time for which the fans will work as they should, and the percentage of probability of fans working more than certain estimated time. Extreme Value Theory can be applied not only for rare and extreme events, but for any event that has values which we can consider as extreme.Keywords: extreme value theory, lifetime, reliability analysis, statistic, time to failure
Procedia PDF Downloads 3261843 Micro-Channel Flows Simulation Based on Nonlinear Coupled Constitutive Model
Authors: Qijiao He
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MicroElectrical-Mechanical System (MEMS) is one of the most rapidly developing frontier research field both in theory study and applied technology. Micro-channel is a very important link component of MEMS. With the research and development of MEMS, the size of the micro-devices and the micro-channels becomes further smaller. Compared with the macroscale flow, the flow characteristics of gas in the micro-channel have changed, and the rarefaction effect appears obviously. However, for the rarefied gas and microscale flow, Navier-Stokes-Fourier (NSF) equations are no longer appropriate due to the breakup of the continuum hypothesis. A Nonlinear Coupled Constitutive Model (NCCM) has been derived from the Boltzmann equation to describe the characteristics of both continuum and rarefied gas flows. We apply the present scheme to simulate continuum and rarefied gas flows in a micro-channel structure. And for comparison, we apply other widely used methods which based on particle simulation or direct solution of distribution function, such as Direct simulation of Monte Carlo (DSMC), Unified Gas-Kinetic Scheme (UGKS) and Lattice Boltzmann Method (LBM), to simulate the flows. The results show that the present solution is in better agreement with the experimental data and the DSMC, UGKS and LBM results than the NSF results in rarefied cases but is in good agreement with the NSF results in continuum cases. And some characteristics of both continuum and rarefied gas flows are observed and analyzed.Keywords: continuum and rarefied gas flows, discontinuous Galerkin method, generalized hydrodynamic equations, numerical simulation
Procedia PDF Downloads 1711842 A Variant of Newton's Method with Free Second-Order Derivative
Authors: Young Hee Geum
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In this paper, we present the iterative method and determine the control parameters to converge cubically for solving nonlinear equations. In addition, we derive the asymptotic error constant.Keywords: asymptotic error constant, iterative method, multiple root, root-finding, order of convergent
Procedia PDF Downloads 2881841 Optimization Method of the Number of Berth at Bus Rapid Transit Stations Based on Passenger Flow Demand
Authors: Wei Kunkun, Cao Wanyang, Xu Yujie, Qiao Yuzhi, Liu Yingning
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The reasonable design of bus parking spaces can improve the traffic capacity of the station and reduce traffic congestion. In order to reasonably determine the number of berths at BRT (Bus Rapid Transit) stops, it is based on the actual bus rapid transit station observation data, scheduling data, and passenger flow data. Optimize the number of station berths from the perspective of optimizing the balance of supply and demand at the site. Combined with the classical capacity calculation model, this paper first analyzes the important factors affecting the traffic capacity of BRT stops by using SPSS PRO and MATLAB programming software, namely the distribution of BRT stops and the distribution of BRT stop time. Secondly, the method of calculating the number of the classic human capital management (HCM) model is optimized based on the actual passenger demand of the station, and the method applicable to the actual number of station berths is proposed. Taking Gangding Station of Zhongshan Avenue Bus Rapid Transit Corridor in Guangzhou as an example, based on the calculation method proposed in this paper, the number of berths of sub-station 1, sub-station 2 and sub-station 3 is 2, which reduces the road space of the station by 33.3% compared with the previous berth 3 of each sub-station, and returns to social vehicles. Therefore, under the condition of ensuring the passenger flow demand of BRT stations, the road space of the station is reduced, and the road is returned to social vehicles, the traffic capacity of social vehicles is improved, and the traffic capacity and efficiency of the BRT corridor system are improved as a whole.Keywords: urban transportation, bus rapid transit station, HCM model, capacity, number of berths
Procedia PDF Downloads 951840 On the convergence of the Mixed Integer Randomized Pattern Search Algorithm
Authors: Ebert Brea
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We propose a novel direct search algorithm for identifying at least a local minimum of mixed integer nonlinear unconstrained optimization problems. The Mixed Integer Randomized Pattern Search Algorithm (MIRPSA), so-called by the author, is based on a randomized pattern search, which is modified by the MIRPSA for finding at least a local minimum of our problem. The MIRPSA has two main operations over the randomized pattern search: moving operation and shrinking operation. Each operation is carried out by the algorithm when a set of conditions is held. The convergence properties of the MIRPSA is analyzed using a Markov chain approach, which is represented by an infinite countable set of state space λ, where each state d(q) is defined by a measure of the qth randomized pattern search Hq, for all q in N. According to the algorithm, when a moving operation is carried out on the qth randomized pattern search Hq, the MIRPSA holds its state. Meanwhile, if the MIRPSA carries out a shrinking operation over the qth randomized pattern search Hq, the algorithm will visit the next state, this is, a shrinking operation at the qth state causes a changing of the qth state into (q+1)th state. It is worthwhile pointing out that the MIRPSA never goes back to any visited states because the MIRPSA only visits any qth by shrinking operations. In this article, we describe the MIRPSA for mixed integer nonlinear unconstrained optimization problems for doing a deep study of its convergence properties using Markov chain viewpoint. We herein include a low dimension case for showing more details of the MIRPSA, when the algorithm is used for identifying the minimum of a mixed integer quadratic function. Besides, numerical examples are also shown in order to measure the performance of the MIRPSA.Keywords: direct search, mixed integer optimization, random search, convergence, Markov chain
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