Search results for: modeling of nonlinear dynamic systems

Authors: Ali Komakpanah, Maryam Yazdi

Abstract:

Few studies have been conducted on polymeric strip and the behavior of soil retaining walls. This paper will present the effect of frequency on the dynamic behavior of reinforced soil retaining walls with polymeric strips. The frequency content describes how the amplitude of a ground motion is distributed among different frequencies. Since the frequency content of an earthquake motion will strongly influence the effects of that motion, the characterization of the motion cannot be completed without the consideration of its frequency content. The maximum axial force of reinforcements and horizontal displacement of the reinforced walls are focused in this research. To clarify the dynamic behavior of reinforced soil retaining walls with polymeric strips, a numerical modeling using Finite Difference Method is benefited. As the results indicate, the frequency of input base acceleration has an important effect on the behavior of these structures. Because of resonant in the system, where the frequency of the input dynamic load is equal to the natural frequency of the system, the maximum horizontal displacement and the maximum axial forces in polymeric strips is occurred. Moreover, they were to increase the structure flexibility because of the main advantages of polymeric strips; i.e. being simple method of construction, having a homogeneous behavior with soils, and possessing long durability, which are of great importance in dynamic analysis.

Keywords: dynamic analysis, frequency, polymeric strip, reinforced soil.

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Authors: Zulaiha Ali Othman, Helmi Md Rais, Abdul Razak Hamdan

Abstract:

Ants are fascinating creatures that demonstrate the ability to find food and bring it back to their nest. Their ability as a colony, to find paths to food sources has inspired the development of algorithms known as Ant Colony Systems (ACS). The principle of cooperation forms the backbone of such algorithms, commonly used to find solutions to problems such as the Traveling Salesman Problem (TSP). Ants communicate to each other through chemical substances called pheromones. Modeling individual ants- ability to manipulate this substance can help an ACS find the best solution. This paper introduces a Dynamic Ant Colony System with threelevel updates (DACS3) that enhance an existing ACS. Experiments were conducted to observe single ant behavior in a colony of Malaysian House Red Ants. Such behavior was incorporated into the DACS3 algorithm. We benchmark the performance of DACS3 versus DACS on TSP instances ranging from 14 to 100 cities. The result shows that the DACS3 algorithm can achieve shorter distance in most cases and also performs considerably faster than DACS.

Keywords: Dynamic Ant Colony System (DACS), Traveling Salesmen Problem (TSP), Optimization, Swarm Intelligent.

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

Abstract:

In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: Grey relational degree, multiple linear regression, membership function, nonlinear programming.

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Authors: A. Udomsakdigool, S. Bangsaranthip

Abstract:

This paper presents an algorithm which combining ant colony optimization in the dynamic programming for solving a dynamic facility layout problem. The problem is separated into 2 phases, static and dynamic phase. In static phase, ant colony optimization is used to find the best ranked of layouts for each period. Then the dynamic programming (DP) procedure is performed in the dynamic phase to evaluate the layout set during multi-period planning horizon. The proposed algorithm is tested over many problems with size ranging from 9 to 49 departments, 2 and 4 periods. The experimental results show that the proposed method is an alternative way for the plant layout designer to determine the layouts during multi-period planning horizon.

Keywords: Ant colony optimization, Dynamicprogramming, Dynamic facility layout planning, Metaheuristic

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Authors: Ryszard Matysiak, Grzegorz Kamieniarz

Abstract:

The deterministic quantum transfer-matrix (QTM) technique and its mathematical background are presented. This important tool in computational physics can be applied to a class of the real physical low-dimensional magnetic systems described by the Heisenberg hamiltonian which includes the macroscopic molecularbased spin chains, small size magnetic clusters embedded in some supramolecules and other interesting compounds. Using QTM, the spin degrees of freedom are accurately taken into account, yielding the thermodynamical functions at finite temperatures. In order to test the application for the susceptibility calculations to run in the parallel environment, the speed-up and efficiency of parallelization are analyzed on our platform SGI Origin 3800 with p = 128 processor units. Using Message Parallel Interface (MPI) system libraries we find the efficiency of the code of 94% for p = 128 that makes our application highly scalable.

Keywords: Deterministic simulations, low-dimensional magnets, modeling of complex systems, parallelization.

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Authors: Sara Sharifi Rad, Hassan Haghighi

Abstract:

Due to important issues, such as deadlock, starvation, communication, non-deterministic behavior and synchronization, concurrent systems are very complex, sensitive, and error-prone. Thus ensuring reliability and accuracy of these systems is very essential. Therefore, there has been a big interest in the formal specification of concurrent programs in recent years. Nevertheless, some features of concurrent systems, such as dynamic process creation, scheduling and starvation have not been specified formally yet. Also, some other features have been specified partially and/or have been described using a combination of several different formalisms and methods whose integration needs too much effort. In other words, a comprehensive and integrated specification that could cover all aspects of concurrent systems has not been provided yet. Thus, this paper makes two major contributions: firstly, it provides a comprehensive formal framework to specify all well-known features of concurrent systems. Secondly, it provides an integrated specification of these features by using just a single formal notation, i.e., the Z language.

Keywords: Concurrent systems, Formal methods, Formal specification, Z language

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Authors: Maya Rupert, Salima Hassas, Carlos Li, John Sherwood

Abstract:

Online Communities are an example of sociallyaware, self-organising, complex adaptive computing systems. The multi-agent systems (MAS) paradigm coordinated by self-organisation mechanisms has been used as an effective way for the simulation and modeling of such systems. In this paper, we propose a model for simulating an online health community using a situated multi-agent system approach, governed by the co-evolution of the social and spatial organisations of the agents.

Keywords: multi-agent systems, organizations, online communities.

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Authors: Mitchell J. McHugh, John J. Case

Abstract:

Systems engineering is a holistic discipline that seeks to organize and optimize complex, interdisciplinary systems. With the growth of artificial intelligence, systems engineers must face the challenge of leveraging artificial intelligence systems to solve complex problems. This paper analyzes the integration of systems engineering and artificial intelligence and discusses how artificial intelligence systems embody the systems decision process (SDP). The SDP is a four-stage problem-solving framework that outlines how systems engineers can design and implement solutions using value-focused thinking. This paper argues that artificial intelligence models can replicate the SDP, thus validating its flexible, value-focused foundation. The authors demonstrate this by developing a machine vision mobile application that can classify weapons to augment the decision-making role of an Army subject matter expert. This practical application was an end-to-end design challenge that highlights how artificial intelligence systems embody systems engineering principles. The impact of this research demonstrates that the SDP is a dynamic tool that systems engineers should leverage when incorporating artificial intelligence within the systems that they develop.

Keywords: Computer vision, machine learning, mobile application, systems engineering, systems decision process.

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Authors: Huihai Wu, Xiaohui Liu

Abstract:

Using Dynamic Bayesian Networks (DBN) to model genetic regulatory networks from gene expression data is one of the major paradigms for inferring the interactions among genes. Averaging a collection of models for predicting network is desired, rather than relying on a single high scoring model. In this paper, two kinds of model searching approaches are compared, which are Greedy hill-climbing Search with Restarts (GSR) and Markov Chain Monte Carlo (MCMC) methods. The GSR is preferred in many papers, but there is no such comparison study about which one is better for DBN models. Different types of experiments have been carried out to try to give a benchmark test to these approaches. Our experimental results demonstrated that on average the MCMC methods outperform the GSR in accuracy of predicted network, and having the comparable performance in time efficiency. By proposing the different variations of MCMC and employing simulated annealing strategy, the MCMC methods become more efficient and stable. Apart from comparisons between these approaches, another objective of this study is to investigate the feasibility of using DBN modeling approaches for inferring gene networks from few snapshots of high dimensional gene profiles. Through synthetic data experiments as well as systematic data experiments, the experimental results revealed how the performances of these approaches can be influenced as the target gene network varies in the network size, data size, as well as system complexity.

Keywords: Genetic regulatory network, Dynamic Bayesian network, GSR, MCMC.

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Authors: Kholod M. Abu-Alnaja

Abstract:

In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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Authors: I. Abuiziah, A. Oulhaj, K. Sebari, D. Ouazar, A. A. Saber

Abstract:

In water pipeline systems, the flow control is an integrated part of the operation, for instance, opening and closing the valves, starting and stopping the pumps, when these operations very quickly performed, they shall cause the hydraulic transient phenomena, which may cause pump and, valve failures and catastrophic pipe ruptures. Fluid transient analysis is one of the more challenging and complicated flow problems in the design and the operation of water pipeline systems. Transient control has become an essential requirement for ensuring safe operation of water pipeline systems. An accurate analysis and suitable protection devices should be used to protect water pipeline systems. The fourth-order Runge-Kutta method has been used to solve the dynamic and continuity equations in the rigid column method, while the characteristics method used to solve these equations in the full elastic methods. This paper presents the problem of modeling and simulating of transient phenomena in conveying pipeline systems based on the rigid column and full elastic methods. Also, it provides the influence of using the protection devices to protect the pipeline systems from damaging due to the gain pressure which occur in the transient state. The results obtained provide that the model is an efficient tool for flow transient analysis and provide approximately identical results by using these two methods. Moreover; using the closed surge tank reduces the unfavorable effects of transients.

Keywords: Flow transient, Pipeline, Air chamber, Numerical model, Protection devices, Elastic method, Rigid column method.

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Authors: Woo Young Jung, Min Ho Kwon, Bu Seog Ju

Abstract:

A failure of the non-structural component can cause  significant damages in critical facilities such as nuclear power plants  and hospitals. Historically, it was reported that the damage from the  leakage of sprinkler systems, resulted in the shutdown of hospitals for  several weeks by the 1971 San Fernando and 1994 North Ridge  earthquakes. In most cases, water leakages were observed at the cross  joints, sprinkler heads, and T-joint connections in piping systems  during and after the seismic events. Hence, the primary objective of  this study was to understand the seismic performance of T-joint  connections and to develop an analytical Finite Element (FE) model  for the T-joint systems of 2-inch fire protection piping system in  hospitals subjected to seismic ground motions. In order to evaluate the  FE models of the piping systems using OpenSees, two types of  materials were used: 1) Steel02 materials and 2) Pinching4 materials.  Results of the current study revealed that the nonlinear  moment-rotation FE models for the threaded T-joint reconciled well  with the experimental results in both FE material models. However,  the system-level fragility determined from multiple nonlinear time  history analyses at the threaded T-joint was slightly different. The  system-level fragility at the T-joint, determined by Pinching4 material  was more conservative than that of using Steel02 material in the piping  system.

Keywords: Fragility, T-joint, Piping, Leakage, Sprinkler.

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Authors: Z. Zainuddin, W. D. Wan Rosli, R. Lanouette, S. Sathasivam

Abstract:

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of pulping problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified odified problem M-1 Ax= M-1b where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

Keywords: Convergence, pulping modeling, neural networks, preconditioned conjugate gradient.

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Authors: Akbar H. Borzabadi, Omid S. Fard

Abstract:

In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming

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Authors: M. Najafi, F. Rahimi Dehgolan

Abstract:

In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.

Keywords: Non-linear vibration, stability, axially moving beam, bifurcation, multiple scales method.

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Authors: Manoj Kumar, A.K. Verma, A. Srividya

Abstract:

Time varying network induced delays in networked control systems (NCS) are known for degrading control system-s quality of performance (QoP) and causing stability problems. In literature, a control method employing modeling of communication delays as probability distribution, proves to be a better method. This paper focuses on modeling of network induced delays as probability distribution. CAN and MIL-STD-1553B are extensively used to carry periodic control and monitoring data in networked control systems. In literature, methods to estimate only the worst-case delays for these networks are available. In this paper probabilistic network delay model for CAN and MIL-STD-1553B networks are given. A systematic method to estimate values to model parameters from network parameters is given. A method to predict network delay in next cycle based on the present network delay is presented. Effect of active network redundancy and redundancy at node level on network delay and system response-time is also analyzed.

Keywords: NCS (networked control system), delay analysis, response-time distribution, worst-case delay, CAN, MIL-STD-1553B, redundancy

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Authors: Ziaddin Daie Koozekanani, Mina Zolfy Lighvan

Abstract:

One of the most challengeable issues in ESL (Electronic System Level) design is the lack of a general modeling scheme for on chip communication architecture. In this paper some of the mostly used methodologies for modeling and representation of on chip communication are investigated. Our goal is studying the existing methods to extract the requirements of a general representation scheme for communication architecture synthesis. The next step, will be introducing a modeling and representation method for being used in automatically synthesis process of on chip communication architecture.

Keywords: Communication architecture, System on Chip, Communication Modeling and Representation

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Authors: Nemat Abazari, Reza Abazari

Abstract:

In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.

Keywords: Nonlinear multi-pantograph equation, delay differential equation, differential transformation method, proportional delay conditions, closed form solution.

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Authors: N. F. F. Ebecken, G. C. Pereira

Abstract:

Ecological systems are exposed and are influenced by various natural and anthropogenic disturbances. They produce various effects and states seeking response symmetry to a state of global phase coherence or stability and balance of their food webs. This research project addresses the development of a computational methodology for modeling plankton food webs. The use of algorithms to establish connections, the generation of representative fuzzy multigraphs and application of technical analysis of complex networks provide a set of tools for defining, analyzing and evaluating community structure of coastal aquatic ecosystems, beyond the estimate of possible external impacts to the networks. Thus, this study aims to develop computational systems and data models to assess how these ecological networks are structurally and functionally organized, to analyze the types and degree of compartmentalization and synchronization between oscillatory and interconnected elements network and the influence of disturbances on the overall pattern of rhythmicity of the system.

Keywords: Ecological networks, plankton food webs, fuzzy multigraphs, dynamic of networks.

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Authors: S. Montenegro, W. Hu

Abstract:

The objective of this paper is to develop a neural network-based residual generator to detect the fault in the actuators for a specific communication satellite in its attitude control system (ACS). First, a dynamic multilayer perceptron network with dynamic neurons is used, those neurons correspond a second order linear Infinite Impulse Response (IIR) filter and a nonlinear activation function with adjustable parameters. Second, the parameters from the network are adjusted to minimize a performance index specified by the output estimated error, with the given input-output data collected from the specific ACS. Then, the proposed dynamic neural network is trained and applied for detecting the faults injected to the wheel, which is the main actuator in the normal mode for the communication satellite. Then the performance and capabilities of the proposed network were tested and compared with a conventional model-based observer residual, showing the differences between these two methods, and indicating the benefit of the proposed algorithm to know the real status of the momentum wheel. Finally, the application of the methods in a satellite ground station is discussed.

Keywords: Satellite, Attitude Control, Momentum Wheel, Neural Network, Fault Detection.

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Authors: C. Senanayake, S. Veera Ragavan

Abstract:

Warehousing is commonly used in factories for the storage of products until delivery of orders. As the amount of products stored increases it becomes tedious to be carried out manually. In recent years, the manual storing has converted into fully or partially computer controlled systems, also known as Automated Storage and Retrieval Systems (AS/RS). This paper discusses an ASRS system, which was designed such that the best storage location for the products is determined by utilizing a fuzzy control system. The design maintains the records of the products to be/already in store and the storage/retrieval times along with the availability status of the storage locations. This paper discusses on the maintenance of the above mentioned records and the utilization of the concept of fuzzy logic in order to determine the optimum storage location for the products. The paper will further discuss on the dynamic splitting and merging of the storage locations depending on the product sizes.

Keywords: ASRS, fuzzy control systems, MySQL database, dynamic splitting and merging.

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Authors: Shishen Xie

Abstract:

In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations

Keywords: variation iteration method, decomposition method, nonlinear integro-differential equations

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Authors: Fares Jnaid, Riyad Aboutaha

Abstract:

In this paper, a nonlinear Finite Element Analysis (FEA) was carried out using ANSYS software to build a model able of predicting the behavior of Reinforced Concrete (RC) beams with unbonded reinforcement. The FEA model was compared to existing experimental data by other researchers. The existing experimental data consisted of 16 beams that varied from structurally sound beams to beams with unbonded reinforcement with different unbonded lengths and reinforcement ratios. The model was able to predict the ultimate flexural strength, load-deflection curve, and crack pattern of concrete beams with unbonded reinforcement. It was concluded that when the when the unbonded length is less than 45% of the span, there will be no decrease in the ultimate flexural strength due to the loss of bond between the steel reinforcement and the surrounding concrete regardless of the reinforcement ratio. Moreover, when the reinforcement ratio is relatively low, there will be no decrease in ultimate flexural strength regardless of the length of unbond.

Keywords: FEA, ANSYS, Unbond, Strain.

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Authors: Kaan T. Oner, Ertugrul Cetinsoy, Efe Sirimoglu, Cevdet Hancer, Taylan Ayken, Mustafa Unel

Abstract:

We present our ongoing work on the development of a new quadrotor aerial vehicle which has a tilt-wing mechanism. The vehicle is capable of take-off/landing in vertical flight mode (VTOL) and flying over long distances in horizontal flight mode. Full dynamic model of the vehicle is derived using Newton-Euler formulation. Linear and nonlinear controllers for the stabilization of attitude of the vehicle and control of its altitude have been designed and implemented via simulations. In particular, an LQR controller has been shown to be quite effective in the vertical flight mode for all possible yaw angles. A sliding mode controller (SMC) with recursive nature has also been proposed to stabilize the vehicle-s attitude and altitude. Simulation results show that proposed controllers provide satisfactory performance in achieving desired maneuvers.

Keywords: UAV, VTOL, dynamic model, stabilization, LQR, SMC

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Authors: G. B. M. Carvalho, V. A. C. Vale, E. T. L. Cöuras Ford

Abstract:

With the aim of increasing the levels of comfort and security structures, the study of dynamic loads on buildings has been one of the focuses in the area of control engineering, civil engineering and architecture. Thus, this work presents a study based on simulation of the dynamics of buildings in the form of portico subjected to wind action, besides presenting an action of passive control, using for this the dynamics of the structure, consequently representing a system appropriated on environmental issues. These control systems are named the dynamic vibration absorbers.

Keywords: Dynamic vibration absorber, structure, comfort, safety, wind behavior, structure.

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Authors: A. N. K. Nasir, M. A. Ahmad, R. M. T. Raja Ismail

Abstract:

The research on two-wheels balancing robot has gained momentum due to their functionality and reliability when completing certain tasks. This paper presents investigations into the performance comparison of Linear Quadratic Regulator (LQR) and PID-PID controllers for a highly nonlinear 2–wheels balancing robot. The mathematical model of 2-wheels balancing robot that is highly nonlinear is derived. The final model is then represented in statespace form and the system suffers from mismatched condition. Two system responses namely the robot position and robot angular position are obtained. The performances of the LQR and PID-PID controllers are examined in terms of input tracking and disturbances rejection capability. Simulation results of the responses of the nonlinear 2–wheels balancing robot are presented in time domain. A comparative assessment of both control schemes to the system performance is presented and discussed.

Keywords: PID, LQR, Two-wheels balancing robot.

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Authors: Pramod Goyal, S. K. Saxena

Abstract:

The convergence of heterogeneous wireless access technologies characterizes the 4G wireless networks. In such converged systems, the seamless and efficient handoff between different access technologies (vertical handoff) is essential and remains a challenging problem. The heterogeneous co-existence of access technologies with largely different characteristics creates a decision problem of determining the “best" available network at “best" time to reduce the unnecessary handoffs. This paper proposes a dynamic decision model to decide the “best" network at “best" time moment to handoffs. The proposed dynamic decision model make the right vertical handoff decisions by determining the “best" network at “best" time among available networks based on, dynamic factors such as “Received Signal Strength(RSS)" of network and “velocity" of mobile station simultaneously with static factors like Usage Expense, Link capacity(offered bandwidth) and power consumption. This model not only meets the individual user needs but also improve the whole system performance by reducing the unnecessary handoffs.

Keywords: Dynamic decision model, Seamless handoff, Vertical handoff, Wireless networks

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Authors: V. Tawiwat, T. Amornthep, P. Pnop

Abstract:

Both the minimum energy consumption and smoothness, which is quantified as a function of jerk, are generally needed in many dynamic systems such as the automobile and the pick-and-place robot manipulator that handles fragile equipments. Nevertheless, many researchers come up with either solely concerning on the minimum energy consumption or minimum jerk trajectory. This research paper considers the indirect minimum Jerk method for higher order differential equation in dynamics optimization proposes a simple yet very interesting indirect jerks approaches in designing the time-dependent system yielding an alternative optimal solution. Extremal solutions for the cost functions of indirect jerks are found using the dynamic optimization methods together with the numerical approximation. This case considers the linear equation of a simple system, for instance, mass, spring and damping. The simple system uses two mass connected together by springs. The boundary initial is defined the fix end time and end point. The higher differential order is solved by Galerkin-s methods weight residual. As the result, the 6th higher differential order shows the faster solving time.

Keywords: Optimization, Dynamic, Linear Systems, Jerks.

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Authors: W. D. Wan Rosli, Z. Zainuddin, R. Lanouette, S. Sathasivam

Abstract:

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of Pulping of Sugar Maple problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified problem where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

Keywords: Convergence, Modeling, Neural Networks, Preconditioned Conjugate Gradient.

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Authors: K. Soldatova, Y. Galerkin

Abstract:

A loading factor performance is necessary for the modeling of centrifugal compressor gas dynamic performance curve. Measured loading factors are linear function of a flow coefficient at an impeller exit. The performance does not depend on the compressibility criterion. To simulate loading factor performances, the authors present two parameters: a loading factor at zero flow rate and an angle between an ordinate and performance line. The calculated loading factor performances of non-viscous are linear too and close to experimental performances. Loading factor performances of several dozens of impellers with different blade exit angles, blade thickness and number, ratio of blade exit/inlet height, and two different type of blade mean line configuration. There are some trends of influence, which are evident – comparatively small blade thickness influence, and influence of geometry parameters is more for impellers with bigger blade exit angles, etc. Approximating equations for both parameters are suggested. The next phase of work will be simulating of experimental performances with the suggested approximation equations as a base.

Keywords: Centrifugal compressor stage, centrifugal compressor, loading factor, gas dynamic performance curve.

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