Search results for: Optimal linear quadratic tracker

Authors: Ruming Yin, Jian Yuan, Qiuhua Yang, Xiuming Shan, Xiqin Wang

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Linear cryptanalysis methods are rarely used to improve the security of chaotic stream ciphers. In this paper, we apply linear cryptanalysis to a chaotic stream cipher which was designed by strictly using the basic design criterion of cryptosystem – confusion and diffusion. We show that this well-designed chaos-based stream cipher is still insecure against distinguishing attack. This distinguishing attack promotes the further improvement of the cipher.

Keywords: Stream cipher, chaos, linear cryptanalysis, distinguishing attack.

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Authors: M. Raciti Castelli, S. De Betta, E. Benini

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The optimal grid spacing and turbulence model for the 2D numerical analysis of a vertical-axis water turbine (VAWaterT) operating in a 2 m/s freestream current has been investigated. The results of five different spatial domain discretizations and two turbulence models (k-ω SST and k-ε RNG) have been compared, in order to gain the optimal y+ parameter distribution along the blade walls during a full rotor revolution. The resulting optimal mesh has appeared to be quite similar to that obtained for the numerical analysis of a vertical-axis wind turbine.

Keywords: CFD, vertical axis water turbine, NACA 0025, blade y+.

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Authors: Hamed Sabahno

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In this paper, an inventory model with finite and constant replenishment rate, price dependant demand rate, time value of money and inflation, finite time horizon, lead time and exponential deterioration rate and with the objective of maximizing the present worth of the total system profit is developed. Using a dynamic programming based solution algorithm, the optimal sequence of the cycles can be found and also different optimal selling prices, optimal order quantities and optimal maximum inventories can be obtained for the cycles with unequal lengths, which have never been done before for this model. Also, a numerical example is used to show accuracy of the solution procedure.

Keywords: Deteriorating items, Dynamic programming, Finitereplenishment rate, Inventory control, Operation Research.

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Authors: Geng Yuan, Yiwan Guo, Fahui Zhai, Shuhua Zhang

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In this paper, we discuss some properties of left spectrum and give the representation of linear preserver map the left spectrum of diagonal quaternionic matrices.

Keywords: Quaternionic matrix, left spectrum, linear preserver map.

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Authors: Ioannis N. Koukoulis, Clio G. Vossou, Christopher G. Provatidis

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The aim of the current work is to present a comparison among three popular optimization methods in the inverse elastostatics problem (IESP) of flaw detection within a solid. In more details, the performance of a simulated annealing, a Hooke & Jeeves and a sequential quadratic programming algorithm was studied in the test case of one circular flaw in a plate solved by both the boundary element (BEM) and the finite element method (FEM). The proposed optimization methods use a cost function that utilizes the displacements of the static response. The methods were ranked according to the required number of iterations to converge and to their ability to locate the global optimum. Hence, a clear impression regarding the performance of the aforementioned algorithms in flaw identification problems was obtained. Furthermore, the coupling of BEM or FEM with these optimization methods was investigated in order to track differences in their performance.

Keywords: Elastostatic, inverse problem, optimization.

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Authors: M. Zamani, O. Kahar

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Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.

Keywords: Navier-Stokes, 'Non-linear grid system', Splitting method.

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Authors: Lazim Abdullah, Nurhakimah Ab. Rahman

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Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.

Keywords: Fuzzy linear systems, Jacobi, Jacobi Over- Relaxation, Refinement of Jacobi, Refinement of Jacobi Over- Relaxation.

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Authors: Shu-Xin Miao

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In this paper, we present an efficient numerical algorithm, namely block homotopy perturbation method, for solving fuzzy linear systems based on homotopy perturbation method. Some numerical examples are given to show the efficiency of the algorithm.

Keywords: Homotopy perturbation method, fuzzy linear systems, block linear system, fuzzy solution, embedding parameter.

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Authors: Xia Cui, Guang-wei Yuan, Jing-yan Yue

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A Picard-Newton iteration method is studied to accelerate the numerical solution procedure of a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. The Picard-Newton iteration is designed by adding higher-order terms of small quantity to an existing Picard iteration. The discrete functional analysis and inductive hypothesis reasoning techniques are used to overcome difficulties coming from nonlinearity and coupling, and theoretical analysis is made for the convergence and approximation properties of the iteration scheme. The Picard-Newton iteration has a quadratic convergent ratio, and its solution has second order spatial approximation and first order temporal approximation to the exact solution of the original problem. Numerical tests verify the results of the theoretical analysis, and show the Picard-Newton iteration is more efficient than the Picard iteration.

Keywords: Nonlinearity, iterative acceleration, coupled parabolic hyperbolic system, quadratic convergence, numerical analysis.

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Authors: Edikan E. Akpanibah, Okwigbedi Oghen’Oro

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In this paper, we studied the optimal portfolio selection in a defined contribution (DC) pension scheme with multiple contributors under constant elasticity of variance (CEV) model and the impact of stochastic additional voluntary contribution on the investment strategies. We assume that the voluntary contributions are stochastic and also consider investments in a risk free asset and a risky asset to increase the expected returns of the contributing members. We derived a stochastic differential equation which consists of the members’ monthly contributions and the invested fund and obtained an optimized problem with the help of Hamilton Jacobi Bellman equation. Furthermore, we find an explicit solution for the optimal investment strategy with stochastic voluntary contribution using power transformation and change of variables method and the corresponding optimal fund size was obtained. We discussed the impact of the voluntary contribution on the optimal investment strategy with numerical simulations and observed that the voluntary contribution reduces the optimal investment strategy of the risky asset.

Keywords: DC pension fund, Hamilton-Jacobi-Bellman, optimal investment strategies, power transformation method, stochastic, voluntary contribution.

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Authors: Rampal Singh, S. Balasundaram

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In this paper, we study the application of Extreme Learning Machine (ELM) algorithm for single layered feedforward neural networks to non-linear chaotic time series problems. In this algorithm the input weights and the hidden layer bias are randomly chosen. The ELM formulation leads to solving a system of linear equations in terms of the unknown weights connecting the hidden layer to the output layer. The solution of this general system of linear equations will be obtained using Moore-Penrose generalized pseudo inverse. For the study of the application of the method we consider the time series generated by the Mackey Glass delay differential equation with different time delays, Santa Fe A and UCR heart beat rate ECG time series. For the choice of sigmoid, sin and hardlim activation functions the optimal values for the memory order and the number of hidden neurons which give the best prediction performance in terms of root mean square error are determined. It is observed that the results obtained are in close agreement with the exact solution of the problems considered which clearly shows that ELM is a very promising alternative method for time series prediction.

Keywords: Chaotic time series, Extreme learning machine, Generalization performance.

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Authors: Jing Zhang, Jie Chen

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In this paper, we deal with the optimal I/O point location in an automated parking system. In this system, the S/R machine (storage and retrieve machine) travels independently in vertical and horizontal directions. Based on the characteristics of the parking system and the basic principle of AS/RS system (Automated Storage and Retrieval System), we obtain the continuous model in units of time. For the single command cycle using the randomized storage policy, we calculate the probability density function for the system travel time and thus we develop the travel time model. And we confirm that the travel time model shows a good performance by comparing with discrete case. Finally in this part, we establish the optimal model by minimizing the expected travel time model and it is shown that the optimal location of the I/O point is located at the middle of the left-hand above corner.

Keywords: Parking system, optimal location, response time, S/R machine.

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Authors: Bin Yu, Minghui Wang, Juntao Zhang

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By the real representation of the quaternionic matrix, an iterative method for quaternionic linear equations Ax = b is proposed. Then the convergence conditions are obtained. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Quaternionic linear equations, Real representation, Iterative algorithm.

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Authors: Marc C. Robini, Pierre-Jean Viverge, Yuemin Zhu, Jianhua Luo

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The standard approach to image reconstruction is to stabilize the problem by including an edge-preserving roughness penalty in addition to faithfulness to the data. However, this methodology produces noisy object boundaries and creates a staircase effect. The existing attempts to favor the formation of smooth contour lines take the edge field explicitly into account; they either are computationally expensive or produce disappointing results. In this paper, we propose to incorporate the smoothness of the edge field in an implicit way by means of an additional penalty term defined in the wavelet domain. We also derive an efficient half-quadratic algorithm to solve the resulting optimization problem, including the case when the data fidelity term is non-quadratic and the cost function is nonconvex. Numerical experiments show that our technique preserves edge sharpness while smoothing contour lines; it produces visually pleasing reconstructions which are quantitatively better than those obtained without wavelet-domain constraints.

Keywords:

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Authors: Daniele Losanno, Giorgio Serino

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This paper focuses on parametric analysis of reinforced concrete structures equipped with supplemental damping braces. Practitioners still luck sufficient data for current design of damper added structures and often reduce the real model to a pure damper braced structure even if this assumption is neither realistic nor conservative. In the present study, the damping brace is modelled as made by a linear supporting brace connected in series with the viscous/hysteretic damper. Deformation capacity of existing structures is usually not adequate to undergo the design earthquake. In spite of this, additional dampers could be introduced strongly limiting structural damage to acceptable values, or in some cases, reducing frame response to elastic behavior. This work is aimed at providing useful considerations for retrofit of existing buildings by means of supplemental damping braces. The study explicitly takes into consideration variability of (a) relative frame to supporting brace stiffness, (b) dampers’ coefficient (viscous coefficient or yielding force) and (c) non-linear frame behavior. Non-linear time history analysis has been run to account for both dampers’ behavior and non-linear plastic hinges modelled by Pivot hysteretic type. Parametric analysis based on previous studies on SDOF or MDOF linear frames provide reference values for nearly optimal damping systems design. With respect to bare frame configuration, seismic response of the damper-added frame is strongly improved, limiting deformations to acceptable values far below ultimate capacity. Results of the analysis also demonstrated the beneficial effect of stiffer supporting braces, thus highlighting inadequacy of simplified pure damper models. At the same time, the effect of variable damping coefficient and yielding force has to be treated as an optimization problem.

Keywords: Brace stiffness, dissipative braces, non-linear analysis, plastic hinges, reinforced concrete.

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Authors: Ehab F. Badran, Guoxiang Gu

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We consider optimal channel equalization for MIMO (multi-input/multi-output) time-varying channels in the sense of MMSE (minimum mean-squared-error), where the observation noise can be non-stationary. We show that all ZF (zero-forcing) receivers can be parameterized in an affine form which eliminates completely the ISI (inter-symbol-interference), and optimal channel equalizers can be designed through minimization of the MSE (mean-squarederror) between the detected signals and the transmitted signals, among all ZF receivers. We demonstrate that the optimal channel equalizer is a modified Kalman filter, and show that under the AWGN (additive white Gaussian noise) assumption, the proposed optimal channel equalizer minimizes the BER (bit error rate) among all possible ZF receivers. Our results are applicable to optimal channel equalization for DWMT (discrete wavelet multitone), multirate transmultiplexers, OFDM (orthogonal frequency division multiplexing), and DS (direct sequence) CDMA (code division multiple access) wireless data communication systems. A design algorithm for optimal channel equalization is developed, and several simulation examples are worked out to illustrate the proposed design algorithm.

Keywords: Channel equalization, Kalman filtering, Time-varying systems.

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Authors: Keny Ordaz-Hernandez, Xavier Fischer, Fouad Bennis

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In a particular case of behavioural model reduction by ANNs, a validity domain shortening has been found. In mechanics, as in other domains, the notion of validity domain allows the engineer to choose a valid model for a particular analysis or simulation. In the study of mechanical behaviour for a cantilever beam (using linear and non-linear models), Multi-Layer Perceptron (MLP) Backpropagation (BP) networks have been applied as model reduction technique. This reduced model is constructed to be more efficient than the non-reduced model. Within a less extended domain, the ANN reduced model estimates correctly the non-linear response, with a lower computational cost. It has been found that the neural network model is not able to approximate the linear behaviour while it does approximate the non-linear behaviour very well. The details of the case are provided with an example of the cantilever beam behaviour modelling.

Keywords: artificial neural network, validity domain, cantileverbeam, non-linear behaviour, model reduction.

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Authors: Tadatsugu Kitamoto

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Recently, a quality of motors is inspected by human ears. In this paper, I propose two systems using a method of speech recognition for automation of the inspection. The first system is based on a method of linear processing which uses K-means and Nearest Neighbor method, and the second is based on a method of non-linear processing which uses neural networks. I used motor sounds in these systems, and I successfully recognize 86.67% of motor sounds in the linear processing system and 97.78% in the non-linear processing system.

Keywords: Acoustical diagnosis, Neural networks, K-means, Short-time Fourier transformation

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

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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: S. J. Hosseini Ghoncheh, M. Paripour

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In this paper the Huang-s method for solving a m×n fuzzy linear system when, m≤ n, is considered. The method in detail is discussed and illustrated by solving some numerical examples.

Keywords: Fuzzy number, fuzzy linear systems, Huang's method.

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Authors: H. Nikzad, S. Yoshitomi

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In this paper, an optimization procedure is applied for 3D Reinforced concrete building structure with shear wall.  In the optimization problem, cross sections of beams, columns and shear wall dimensions are considered as design variables and the optimal cross sections can be derived to minimize the total cost of the structure. As for final design application, the most suitable sections are selected to satisfy ACI 318-14 code provision based on static linear analysis. The validity of the method is examined through numerical example of 15 storied 3D RC building with shear wall.  This optimization method is expected to assist in providing a useful reference in design early stage, and to be an effective and powerful tool for structural design of RC shear wall structures.

Keywords: Structural optimization, linear static analysis, ETABS, MATLAB, RC moment frame, RC shear wall structures.

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Authors: Rabiˆı DARITI, El Mamoun SOUIDI

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Linear error-block codes are a natural generalization of linear error correcting codes. The purpose of this paper is to generalize some results on the packing and the covering radii to the error-block case. We study their properties when a code undergoes some specific modifications and combinations with another code. We give a few bounds on the packing and the covering radii of these codes.

Keywords: Linear error-block codes, π-distance, Correction capacity, Packing radius, Covering radius.

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Authors: Quoc Khanh Dang, Thomas Bourdeaud’huy, Khaled Mesghouni, Armand Toguy´eni

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This paper studies a train routing and scheduling problem for busy railway stations. Our objective is to allow trains to be routed in dense areas that are reaching saturation. Unlike traditional methods that allocate all resources to setup a route for a train and until the route is freed, our work focuses on the use of resources as trains progress through the railway node. This technique allows a larger number of trains to be routed simultaneously in a railway node and thus reduces their current saturation. To deal with this problem, this study proposes an abstract model and a mixed-integer linear programming formulation to solve it. The applicability of our method is illustrated on a didactic example.

Keywords: Busy railway stations, mixed-integer linear programming, offline railway station management, train platforming, train routing, train scheduling.

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Authors: Pradip Deb

Abstract:

Quantitative radiobiological models can be used to assess the optimum clinical outcome from sophisticated therapeutic modalities by calculating tumor control probability (TCP) and normal tissue complication probability (NTCP). In this study two 3D-CRT and an IMRT treatment plans were developed with an initial prescription dose of 60 Gy in 2 Gy/fraction to prostate. Sensitivity of TCP and Complication free tumor control probability (P+) to the different values of α/β ratio was investigated for various prescription doses planned to be delivered in either a fixed number of fractions (I) or in a fixed dose per fraction (II) in each of the three different treatment plans. High dose/fraction and high α/β value result in comparatively smaller P+ and IMRT plans resulted in the highest P+, mainly due to the decrease in NTCP. If α/β is lower than expected, better tumor control can be achieved by increasing dose/fraction but decreasing the number of fractions.

Keywords: Linear Quadratic Model, TCP, NTCP, α/β ratio.

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Authors: Alia Alghosoun, Ashraf Osman, Mohammed Seaid

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A coupled two-layer finite volume/finite element method was proposed for solving dam-break flow problem over deformable beds. The governing equations consist of the well-balanced two-layer shallow water equations for the water flow and a linear elastic model for the bed deformations. Deformations in the topography can be caused by a brutal localized force or simply by a class of sliding displacements on the bathymetry. This deformation in the bed is a source of perturbations, on the water surface generating water waves which propagate with different amplitudes and frequencies. Coupling conditions at the interface are also investigated in the current study and two mesh procedure is proposed for the transfer of information through the interface. In the present work a new procedure is implemented at the soil-water interface using the finite element and two-layer finite volume meshes with a conservative distribution of the forces at their intersections. The finite element method employs quadratic elements in an unstructured triangular mesh and the finite volume method uses the Rusanove to reconstruct the numerical fluxes. The numerical coupled method is highly efficient, accurate, well balanced, and it can handle complex geometries as well as rapidly varying flows. Numerical results are presented for several test examples of dam-break flows over deformable beds. Mesh convergence study is performed for both methods, the overall model provides new insight into the problems at minimal computational cost.

Keywords: Dam-break flows, deformable beds, finite element method, finite volume method, linear elasticity, Shallow water equations.

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Authors: Xiang Zhang, David Rey, S. Travis Waller

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Stochastic User Equilibrium (SUE) model is a widely used traffic assignment model in transportation planning, which is regarded more advanced than Deterministic User Equilibrium (DUE) model. However, a problem exists that the performance of the SUE model depends on its error term parameter. The objective of this paper is to propose a systematic method of determining the appropriate error term parameter value for the SUE model. First, the significance of the parameter is explored through a numerical example. Second, the parameter calibration method is developed based on the Logit-based route choice model. The calibration process is realized through multiple nonlinear regression, using sequential quadratic programming combined with least square method. Finally, case analysis is conducted to demonstrate the application of the calibration process and validate the better performance of the SUE model calibrated by the proposed method compared to the SUE models under other parameter values and the DUE model.

Keywords: Parameter calibration, sequential quadratic programming, Stochastic User Equilibrium, traffic assignment, transportation planning.

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Authors: Promise A. Azor, Avievie Igodo, Esabai M. Ase

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The paper merged the return of premium clause and voluntary contributions to investigate retirees’ investment plan in a defined contributory (DC) pension scheme with a portfolio comprising of a risk-free asset and a risky asset whose price process is described by geometric Brownian motion (GBM). The paper considers additional voluntary contributions paid by members, charge on balance by pension fund administrators and the mortality risk of members of the scheme during the accumulation period by introducing return of premium clause. To achieve this, the Weilbull mortality force function is used to establish the mortality rate of members during accumulation phase. Furthermore, an optimization problem from the Hamilton Jacobi Bellman (HJB) equation is obtained using dynamic programming approach. Also, the Legendre transformation method is used to transform the HJB equation which is a nonlinear partial differential equation to a linear partial differential equation and solves the resultant equation for the value function and the optimal distribution plan under logarithm utility function. Finally, numerical simulations of the impact of some important parameters on the optimal distribution plan were obtained and it was observed that the optimal distribution plan is inversely proportional to the initial fund size, predetermined interest rate, additional voluntary contributions, charge on balance and instantaneous volatility.

Keywords: Legendre transform, logarithm utility, optimal distribution plan, return clause of premium, charge on balance, Weibull mortality function.

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Authors: Edikan E. Akpanibah Obinichi C. Mandah Imoleayo S. Asiwaju

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In this paper, we studied the effect of supplementary premium on the optimal portfolio policy in a defined contribution (DC) pension scheme with refund of premium clauses. This refund clause allows death members’ next of kin to withdraw their relative’s accumulated wealth during the accumulation period. The supplementary premium is to help sustain the scheme and is assumed to be stochastic. We considered cases when the remaining wealth is equally distributed and when it is not equally distributed among the remaining members. Next, we considered investments in cash and equity to help increase the remaining accumulated funds to meet up with the retirement needs of the remaining members and composed the problem as a continuous time mean-variance stochastic optimal control problem using the actuarial symbol and established an optimization problem from the extended Hamilton Jacobi Bellman equations. The optimal portfolio policy, the corresponding optimal fund size for the two assets and also the efficient frontier of the pension members for the two cases was obtained. Furthermore, the numerical simulations of the optimal portfolio policies with time were presented and the effect of the supplementary premium on the optimal portfolio policy was discussed and observed that the supplementary premium decreases the optimal portfolio policy of the risky asset (equity). Secondly we observed a disparity between the optimal policies for the two cases.

Keywords: Defined contribution pension scheme, extended Hamilton Jacobi Bellman equations, optimal portfolio policies, refund of premium clauses, supplementary premium.

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Authors: Ekow A. Kwofie, Emmanuel K. Anto, Godfred Mensah

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In this paper, CYME Distribution software has been used to assess the impacts of solar Photovoltaic (PV) distributed generation (DG) plant on the Electricity Company of Ghana (ECG) 33 kV sub-transmission network at different PV penetration levels. As ECG begins to encourage DG PV interconnections within its network, there has been the need to assess the impacts on the sub-transmission losses and voltage contribution. In Tema, a city in Accra - Ghana, ECG has a 33 kV sub-transmission network made up of 20 No. 33 kV buses that was modeled. Three different locations were chosen: The source bus, a bus along the sub-transmission radial network and a bus at the tail end to determine the optimal location for DG PV interconnection. The optimal location was determined based on sub-transmission technical losses and voltage impact. PV capacities at different penetration levels were modeled at each location and simulations performed to determine the optimal PV penetration level. Interconnection at a bus along (or in the middle of) the sub-transmission network offered the highest benefits at an optimal PV penetration level of 80%. At that location, the maximum voltage improvement of 0.789% on the neighboring 33 kV buses and maximum loss reduction of 6.033% over the base case scenario were recorded. Hence, the optimal location for DG PV integration within the 33 kV sub-transmission utility network is at a bus along the sub-transmission radial network.

Keywords: Distributed generation photovoltaic, DG PV, optimal location, penetration level, sub-transmission network.

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Authors: N. Rugthaicharoencheep, S. Auchariyamet

Abstract:

Optimal capacitor allocation in distribution systems has been studied for a long times. It is an optimization problem which has an objective to define the optimal sizes and locations of capacitors to be installed. In this works, an overview of capacitor placement problem in distribution systems is briefly introduced. The objective functions and constraints of the problem are listed and the methodologies for solving the problem are summarized.

Keywords: Capacitor Placement, Distribution Systems, Optimization Techniques

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