Search results for: discrete method

Authors: Abdulnasir Hossen, Ulrich Heute

Abstract:

In 1990 [1] the subband-DFT (SB-DFT) technique was proposed. This technique used the Hadamard filters in the decomposition step to split the input sequence into low- and highpass sequences. In the next step, either two DFTs are needed on both bands to compute the full-band DFT or one DFT on one of the two bands to compute an approximate DFT. A combination network with correction factors was to be applied after the DFTs. Another approach was proposed in 1997 [2] for using a special discrete wavelet transform (DWT) to compute the discrete Fourier transform (DFT). In the first step of the algorithm, the input sequence is decomposed in a similar manner to the SB-DFT into two sequences using wavelet decomposition with Haar filters. The second step is to perform DFTs on both bands to obtain the full-band DFT or to obtain a fast approximate DFT by implementing pruning at both input and output sides. In this paper, the wavelet-based DFT (W-DFT) with Haar filters is interpreted as SB-DFT with Hadamard filters. The only difference is in a constant factor in the combination network. This result is very important to complete the analysis of the W-DFT, since all the results concerning the accuracy and approximation errors in the SB-DFT are applicable. An application example in spectral analysis is given for both SB-DFT and W-DFT (with different filters). The adaptive capability of the SB-DFT is included in the W-DFT algorithm to select the band of most energy as the band to be computed. Finally, the W-DFT is extended to the two-dimensional case. An application in image transformation is given using two different types of wavelet filters.

Keywords: Image Transform, Spectral Analysis, Sub-Band DFT, Wavelet DFT.

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Authors: Zhengsheng Wang, Jing Qi, Chuntao Liu, Yuanjun Li

Abstract:

The harmonic Arnoldi method can be used to find interior eigenpairs of large matrices. However, it has been shown that this method may converge erratically and even may fail to do so. In this paper, we present a new method for computing interior eigenpairs of large nonsymmetric matrices, which is called weighted harmonic Arnoldi method. The implementation of the method has been tested by numerical examples, the results show that the method converges fast and works with high accuracy.

Keywords: Harmonic Arnoldi method, weighted harmonic Arnoldi method, eigenpair, interior eigenproblem, non symmetric matrix.

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Authors: I-Ling Chang, Jer-An Chen

Abstract:

The elastic properties and fracture of two-dimensional graphene were calculated purely from the atomic bonding (stretching and bending) based on molecular mechanics method. Considering the representative unit cell of graphene under various loading conditions, the deformations of carbon bonds and the variations of the interlayer distance could be realized numerically under the geometry constraints and minimum energy assumption. In elastic region, it was found that graphene was in-plane isotropic. Meanwhile, the in-plane deformation of the representative unit cell is not uniform along armchair direction due to the discrete and non-uniform distributions of the atoms. The fracture of graphene could be predicted using fracture criteria based on the critical bond length, over which the bond would break. It was noticed that the fracture behavior were directional dependent, which was consistent with molecular dynamics simulation results.

Keywords: Energy minimization, fracture, graphene, molecular mechanics.

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Authors: Jin Sup Kim, Woo Young Jung, Minho Kwon

Abstract:

In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC α-method to compare that with dissipation method and Newmark method through the stability analysis and numerical example. PC α-method gives more accuracy than other methods because it based on the α-method inherits the superior properties of the implicit α-method. In finite element analysis, the PC α-method is more useful than other methods because it is the explicit scheme and it achieves the second order accuracy and numerical damping simultaneously.

Keywords: Dynamic, α-Method, P-Method, PC α-Method, Newmark method.

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Authors: Mohsen A. Bakouri, Andrey V. Savkin, Abdul-Hakeem H. Alomari, Robert F. Salamonsen, Einly Lim, Nigel H. Lovell

Abstract:

Physiological control of a left ventricle assist device (LVAD) is generally a complicated task due to diverse operating environments and patient variability. In this work, a tracking control algorithm based on sliding mode and feed forward control for a class of discrete-time single input single output (SISO) nonlinear uncertain systems is presented. The controller was developed to track the reference trajectory to a set operating point without inducing suction in the ventricle. The controller regulates the estimated mean pulsatile flow Qp and mean pulsatility index of pump rotational speed PIω that was generated from a model of the assist device. We recall the principle of the sliding mode control theory then we combine the feed-forward control design with the sliding mode control technique to follow the reference trajectory. The uncertainty is replaced by its upper and lower boundary. The controller was tested in a computer simulation covering two scenarios (preload and ventricular contractility). The simulation results prove the effectiveness and the robustness of the proposed controller

Keywords: robust control system, discrete-sliding mode, left ventricularle assist devicse, pulsatility index.

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Authors: Magdy B. Eteiba, Wael Ismael Wahba, Shimaa Barakat

Abstract:

This paper presents a fault identification, classification and fault location estimation method based on Discrete Wavelet Transform and Adaptive Network Fuzzy Inference System (ANFIS) for medium voltage cable in the distribution system.

Different faults and locations are simulated by ATP/EMTP, and then certain selected features of the wavelet transformed signals are used as an input for a training process on the ANFIS. Then an accurate fault classifier and locator algorithm was designed, trained and tested using current samples only. The results obtained from ANFIS output were compared with the real output. From the results, it was found that the percentage error between ANFIS output and real output is less than three percent. Hence, it can be concluded that the proposed technique is able to offer high accuracy in both of the fault classification and fault location.

Keywords: ANFIS, Fault location, Underground Cable, Wavelet Transform.

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Authors: Sunitha S. L., V. Udayashankara

Abstract:

Hearing impairment is the number one chronic disability affecting many people in the world. Background noise is particularly damaging to speech intelligibility for people with hearing loss especially for sensorineural loss patients. Several investigations on speech intelligibility have demonstrated sensorineural loss patients need 5-15 dB higher SNR than the normal hearing subjects. This paper describes Discrete Hartley Transform Power Normalized Least Mean Square algorithm (DHT-LMS) to improve the SNR and to reduce the convergence rate of the Least Means Square (LMS) for sensorineural loss patients. The DHT transforms n real numbers to n real numbers, and has the convenient property of being its own inverse. It can be effectively used for noise cancellation with less convergence time. The simulated result shows the superior characteristics by improving the SNR at least 9 dB for input SNR with zero dB and faster convergence rate (eigenvalue ratio 12) compare to time domain method and DFT-LMS.

Keywords: Hearing Impairment, DHT-LMS, Convergence rate, SNR improvement.

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Authors: Liudmyla Koliechkina, Olena Dvirna

Abstract:

The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: Discrete set, linear combinatorial optimization, multi-objective optimization, multipermutation, Pareto solutions, partial permutation set, permutation, structural graph.

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Authors: Mehdi Seifbarghy, Sajjad Jalali, Seyed Habib A. Rahmati

Abstract:

This paper provides a framework in order to incorporate reliability issue as a sign of disruption in distribution systems and partial covering theory as a response to limitation in coverage radios and economical preferences, simultaneously into the traditional literatures of capacitated facility location problems. As a result we develop a bi-objective model based on the discrete scenarios for expected cost minimization and demands coverage maximization through a three echelon supply chain network by facilitating multi-capacity levels for provider side layers and imposing gradual coverage function for distribution centers (DCs). Additionally, in spite of objectives aggregation for solving the model through LINGO software, a branch of LP-Metric method called Min- Max approach is proposed and different aspects of corresponds model will be explored.

Keywords: Reliability Cost, Partial Covering, LP-Metric

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Authors: Sana Ktata, Kaïs Ouni, Noureddine Ellouze

Abstract:

Electrocardiogram (ECG) data compression algorithm is needed that will reduce the amount of data to be transmitted, stored and analyzed, but without losing the clinical information content. A wavelet ECG data codec based on the Set Partitioning In Hierarchical Trees (SPIHT) compression algorithm is proposed in this paper. The SPIHT algorithm has achieved notable success in still image coding. We modified the algorithm for the one-dimensional (1-D) case and applied it to compression of ECG data. By this compression method, small percent root mean square difference (PRD) and high compression ratio with low implementation complexity are achieved. Experiments on selected records from the MIT-BIH arrhythmia database revealed that the proposed codec is significantly more efficient in compression and in computation than previously proposed ECG compression schemes. Compression ratios of up to 48:1 for ECG signals lead to acceptable results for visual inspection.

Keywords: Discrete Wavelet Transform, ECG compression, SPIHT.

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Authors: Jason Chien-Hsun Tseng, Nguyen Dong-Thai Dao, Chong-Ching Chang

Abstract:

A novel PDE solver using the multidimensional wave digital filtering (MDWDF) technique to achieve the solution of a 2D seismic wave system is presented. In essence, the continuous physical system served by a linear Kirchhoff circuit is transformed to an equivalent discrete dynamic system implemented by a MD wave digital filtering (MDWDF) circuit. This amounts to numerically approximating the differential equations used to describe elements of a MD passive electronic circuit by a grid-based difference equations implemented by the so-called state quantities within the passive MDWDF circuit. So the digital model can track the wave field on a dense 3D grid of points. Details about how to transform the continuous system into a desired discrete passive system are addressed. In addition, initial and boundary conditions are properly embedded into the MDWDF circuit in terms of state quantities. Graphic results have clearly demonstrated some physical effects of seismic wave (P-wave and S–wave) propagation including radiation, reflection, and refraction from and across the hard boundaries. Comparison between the MDWDF technique and the finite difference time domain (FDTD) approach is also made in terms of the computational efficiency.

Keywords: Seismic Wave Propagation, Multi-dimension WaveDigital Filters, Partial Differential Equations.

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Authors: González-Izal M., Rodríguez-Carreño I, Mallor-Giménez F, Malanda A, Izquierdo M

Abstract:

The purpose of this study was to evaluate and compare new indices based on the discrete wavelet transform with another spectral parameters proposed in the literature as mean average voltage, median frequency and ratios between spectral moments applied to estimate acute exercise-induced changes in power output, i.e., to assess peripheral muscle fatigue during a dynamic fatiguing protocol. 15 trained subjects performed 5 sets consisting of 10 leg press, with 2 minutes rest between sets. Surface electromyography was recorded from vastus medialis (VM) muscle. Several surface electromyographic parameters were compared to detect peripheral muscle fatigue. These were: mean average voltage (MAV), median spectral frequency (Fmed), Dimitrov spectral index of muscle fatigue (FInsm5), as well as other five parameters obtained from the discrete wavelet transform (DWT) as ratios between different scales. The new wavelet indices achieved the best results in Pearson correlation coefficients with power output changes during acute dynamic contractions. Their regressions were significantly different from MAV and Fmed. On the other hand, they showed the highest robustness in presence of additive white gaussian noise for different signal to noise ratios (SNRs). Therefore, peripheral impairments assessed by sEMG wavelet indices may be a relevant factor involved in the loss of power output after dynamic high-loading fatiguing task.

Keywords: Median Frequency, EMG, wavelet transform, muscle fatigue

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Authors: Andrey V. Timofeev

Abstract:

This paper introduces an original method for guaranteed estimation of the accuracy for an ensemble of Lipschitz classifiers. The solution was obtained as a finite closed set of alternative hypotheses, which contains an object of classification with probability of not less than the specified value. Thus, the classification is represented by a set of hypothetical classes. In this case, the smaller the cardinality of the discrete set of hypothetical classes is, the higher is the classification accuracy. Experiments have shown that if cardinality of the classifiers ensemble is increased then the cardinality of this set of hypothetical classes is reduced. The problem of the guaranteed estimation of the accuracy for an ensemble of Lipschitz classifiers is relevant in multichannel classification of target events in C-OTDR monitoring systems. Results of suggested approach practical usage to accuracy control in C-OTDR monitoring systems are present.

Keywords: Lipschitz classifiers, confidence set, C-OTDR monitoring, classifiers accuracy, classifiers ensemble.

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Authors: L. Hermanns, M.A. Santoyo, L. E. Quirós, J. Vega, J. M. Gaspar-Escribano, B. Benito

Abstract:

We study the dynamic response of a wind turbine structure subjected to theoretical seismic motions, taking into account the rotational component of ground shaking. Models are generated for a shallow moderate crustal earthquake in the Madrid Region (Spain). Synthetic translational and rotational time histories are computed using the Discrete Wavenumber Method, assuming a point source and a horizontal layered earth structure. These are used to analyze the dynamic response of a wind turbine, represented by a simple finite element model. Von Mises stress values at different heights of the tower are used to study the dynamical structural response to a set of synthetic ground motion time histories

Keywords: Synthetic seismograms, rotations, wind turbine, dynamic structural response

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Authors: Hamidreza Akbari

Abstract:

In this paper, for detection of inclined eccentricity in an induction motor, time–frequency analysis of the stator startup current is carried out. For this purpose, the discrete wavelet transform is used. Data are obtained from simulations, using winding function approach. The results show the validity of the approach for detecting the fault and discriminating with respect to other faults.

Keywords: Induction machine, Fault, DWT.

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Authors: Nabli L., Dhouibi H., Collart Dutilleul S., Craye E.

Abstract:

The existence of maximal durations drastically modifies the performance evaluation in Discrete Event Systems (DES). The same particularity may be found on systems where the associated constraints do not concern the time. For example weight measures, in chemical industry, are used in order to control the quantity of consumed raw materials. This parameter also takes a fundamental part in the product quality as the correct transformation process is based upon a given percentage of each essence. Weight regulation therefore increases the global productivity of the system by decreasing the quantity of rejected products. In this paper we present an approach based on mixing different characteristics theories, the fuzzy system and Petri net system to describe the behaviour. An industriel application on a tobacco manufacturing plant, where the critical parameter is the weight is presented as an illustration.

Keywords: Petri Net, Manufacturing systems, Performance evaluation, Fuzzy logic, Tolerant system.

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Authors: A. Idawaty, O. Mohamed, A. Z. Zuriati

Abstract:

This paper presents the development of an event based Discrete Event Simulation (DES) for a recovery algorithm known Backward Recovery Global Preemptive Utility Accrual Scheduling (BR_GPUAS). This algorithm implements the Backward Recovery (BR) mechanism as a fault recovery solution under the existing Time/Utility Function/ Utility Accrual (TUF/UA) scheduling domain for multiprocessor environment. The BR mechanism attempts to take the faulty tasks back to its initial safe state and then proceeds to re-execute the affected section of the faulty tasks to enable recovery. Considering that faults may occur in the components of any system; a fault tolerance system that can nullify the erroneous effect is necessary to be developed. Current TUF/UA scheduling algorithm uses the abortion recovery mechanism and it simply aborts the erroneous task as their fault recovery solution. None of the existing algorithm in TUF/UA scheduling domain in multiprocessor scheduling environment have considered the transient fault and implement the BR mechanism as a fault recovery mechanism to nullify the erroneous effect and solve the recovery problem in this domain. The developed BR_GPUAS simulator has derived the set of parameter, events and performance metrics according to a detailed analysis of the base model. Simulation results revealed that BR_GPUAS algorithm can saved almost 20-30% of the accumulated utilities making it reliable and efficient for the real-time application in the multiprocessor scheduling environment.

Keywords: Time Utility Function/ Utility Accrual (TUF/UA) scheduling, Real-time system (RTS), Backward Recovery, Multiprocessor, Discrete Event Simulation (DES).

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Authors: J.S.C. Prentice

Abstract:

The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

Keywords: RK1GL2X3, RK1GL2, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, local error, global error.

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Authors: Kamand Bagherian, Nariman Niknejad

Abstract:

A vibration isolation technology for precise position control of a rotary system powered by two permanent magnet DC (PMDC) motors is proposed, where this system is mounted on an oscillatory frame. To achieve vibration isolation for this system, active damping and disturbance rejection (ADDR) technology is presented which introduces a cooperation of a main and an auxiliary PMDC, controlled by discrete-time sliding mode control (DTSMC) based schemes. The controller of the main actuator tracks a desired position and the auxiliary actuator simultaneously isolates the induced vibration, as its controller follows a torque trend. To determine this torque trend, a combination of two algorithms is introduced by the ADDR technology. The first torque-trend producing algorithm rejects the disturbance by counteracting the perturbation, estimated using a model-based observer. The second torque trend applies active variable damping to minimize the oscillation of the output shaft. In this practice, the presented technology is implemented on a rotary system with a pendulum attached, mounted on a linear actuator simulating an oscillation-transmitting structure. In addition, the obtained results illustrate the functionality of the proposed technology.

Keywords: Vibration isolation, position control, discrete-time nonlinear controller, active damping, disturbance tracking algorithm, oscillation transmitting support, stability robustness.

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Authors: B. X. Tchomeni, A. A. Alugongo, T. B. Tengen

Abstract:

In this paper, de Laval rotor system has been characterized by a hinge model and its transient response numerically treated for a dynamic solution. The effect of the ensuing non-linear disturbances namely rub and breathing crack is numerically simulated. Subsequently, three analysis methods: Orbit Analysis, Fast Fourier Transform (FFT), and Wavelet Transform (WT) are employed to extract features of the vibration signal of the faulty system. An analysis of the system response orbits clearly indicates the perturbations due to the rotor-to-stator contact. The sensitivities of WT to the variation in system speed have been investigated by Continuous Wavelet Transform (CWT). The analysis reveals that features of crack, rubs and unbalance in vibration response can be useful for condition monitoring. WT reveals its ability to detect nonlinear signal, and obtained results provide a useful tool method for detecting machinery faults.

Keywords: Continuous wavelet, crack, discrete wavelet, high acceleration, low acceleration, nonlinear, rotor-stator, rub.

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Authors: Mohammed Salem Alzahrani

Abstract:

In this paper the optimality of the solution of an existing real word assignment problem known as the seat assignment problem using Seat Assignment Method (SAM) is discussed. SAM is the newly driven method from three existing methods, Hungarian Method, Northwest Corner Method and Least Cost Method in a special way that produces the easiness & fairness among all methods that solve the seat assignment problem.

Keywords: Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM), A Real Word Assignment Problem.

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Authors: A. Basiri, S. Rahmany, D. Khatibi

Abstract:

The aim of this paper is to review some of standard fact on Miura curves. We give some easy theorem in number theory to define Miura curves, then we present a new implementation of Arita algorithm for Miura curves.

Keywords: Miura curve, discrete logarithm problem, algebraic curve cryptography, Jacobian group.

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Authors: R. Sahraian, A. Karampour Haghighi, E. Ghasemi

Abstract:

Process planning and production scheduling play important roles in manufacturing systems. In this paper a multiobjective mixed integer linear programming model is presented for the integrated planning and scheduling of multi-product. The aim is to find a set of high-quality trade-off solutions. This is a combinatorial optimization problem with substantially large solution space, suggesting that it is highly difficult to find the best solutions with the exact search method. To account for it, a PSO-based algorithm is proposed by fully utilizing the capability of the exploration search and fast convergence. To fit the continuous PSO in the discrete modeled problem, a solution representation is used in the algorithm. The numerical experiments have been performed to demonstrate the effectiveness of the proposed algorithm.

Keywords: Integrated process planning and scheduling, multi objective, MILP, Particle swarm optimization

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Authors: Smriti H. Bhandari, S. M. Deshpande

Abstract:

Surface metrology with image processing is a challenging task having wide applications in industry. Surface roughness can be evaluated using texture classification approach. Important aspect here is appropriate selection of features that characterize the surface. We propose an effective combination of features for multi-scale and multi-directional analysis of engineering surfaces. The features include standard deviation, kurtosis and the Canny edge detector. We apply the method by analyzing the surfaces with Discrete Wavelet Transform (DWT) and Dual-Tree Complex Wavelet Transform (DT-CWT). We used Canberra distance metric for similarity comparison between the surface classes. Our database includes the surface textures manufactured by three machining processes namely Milling, Casting and Shaping. The comparative study shows that DT-CWT outperforms DWT giving correct classification performance of 91.27% with Canberra distance metric.

Keywords: Dual-tree complex wavelet transform, surface metrology, surface roughness, texture classification.

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Authors: P. Vazan, P. Tanuska

Abstract:

The paper provides the basic overview of simulation optimization. The procedure of its practical using is demonstrated on the real example in simulator Witness. The simulation optimization is presented as a good tool for solving many problems in real praxis especially in production systems. The authors also characterize their own experiences and they mention the strengths and weakness of simulation optimization.

Keywords: discrete event simulation, simulation optimization, Witness

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Authors: Jean Berger, Nassirou Lo, Martin Noel

Abstract:

Perfectly suited for natural or man-made emergency and disaster management situations such as flood, earthquakes, tornadoes, or tsunami, multi-target search path planning for a team of rescue agents is known to be computationally hard, and most techniques developed so far come short to successfully estimate optimality gap. A novel mixed-integer linear programming (MIP) formulation is proposed to optimally solve the multi-target multi-agent discrete search and rescue (SAR) path planning problem. Aimed at maximizing cumulative probability of successful target detection, it captures anticipated feedback information associated with possible observation outcomes resulting from projected path execution, while modeling agent discrete actions over all possible moving directions. Problem modeling further takes advantage of network representation to encompass decision variables, expedite compact constraint specification, and lead to substantial problem-solving speed-up. The proposed MIP approach uses CPLEX optimization machinery, efficiently computing near-optimal solutions for practical size problems, while giving a robust upper bound obtained from Lagrangean integrality constraint relaxation. Should eventually a target be positively detected during plan execution, a new problem instance would simply be reformulated from the current state, and then solved over the next decision cycle. A computational experiment shows the feasibility and the value of the proposed approach.

Keywords: Search path planning, search and rescue, multi-agent, mixed-integer linear programming, optimization.

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Authors: K. Kaabeche-Djerafi, N. Bendjaballah-Lalaoui, S. Semra

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The paper aims at investigating influence of medium capacity on linear adsorbed solute dispersion into chemically heterogeneous fixed beds. A discrete chemical heterogeneity distribution is considered in the one-dimensional advectivedispersive equation. The partial differential equation is solved using finite volumes method based on the Adam-Bashforth algorithm. Increased dispersion is estimated by comparing breakthrough curves second order moments and keeping identical hydrodynamic properties. As a result, dispersion increase due to chemical heterogeneity depends on the column size and surprisingly on the solid capacity. The more intense capacity is, the more important solute dispersion is. Medium length which is known to favour this effect vanishing according to the linear adsorption in fixed bed seems to create nonmonotonous variation of dispersion because of the heterogeneity. This nonmonotonous behaviour is also favoured by high capacities.

Keywords: linear adsorption; chemical heterogeneity;dispersion; fixed bed; porous media

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Authors: Seifedine Kadry

Abstract:

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.

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Authors: Aritras Roy, Rinku Mukherjee

Abstract:

The current study couples a quasi-steady Vortex Lattice Method and a camber correcting technique, ‘Decambering’ for unsteady post-stall flow prediction. The wake is force-free and discrete such that the wake lattices move with the free-stream once shed from the wing. It is observed that the time-averaged unsteady coefficient of lift sees a relative drop at post-stall angles of attack in comparison to its steady counterpart for some angles of attack. Multiple solutions occur at post-stall and three different algorithms to choose solutions in these regimes show both unsteadiness and non-convergence of the iterations. The distribution of coefficient of lift on the wing span also shows sawtooth. Distribution of vorticity changes both along span and in the direction of the free-stream as the wake develops over time with distinct roll-up, which increases with time.

Keywords: Post-stall, unsteady, wing, aerodynamics.

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Authors: Tirthankar Ghosh, Dilip Roy, Nimai Kumar Chandra

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Sometime it is difficult to determine the exact reliability for complex systems in analytical procedures. Approximate solution of this problem can be provided through discretization of random variables. In this paper we describe the usefulness of discretization of a random variable using the reversed hazard rate function of its continuous version. Discretization of the exponential distribution has been demonstrated. Applications of this approach have also been cited. Numerical calculations indicate that the proposed approach gives very good approximation of reliability of complex systems under stress-strength set-up. The performance of the proposed approach is better than the existing discrete concentration method of discretization. This approach is conceptually simple, handles analytic intractability and reduces computational time. The approach can be applied in manufacturing industries for producing high-reliable items.

Keywords: Discretization, Reversed Hazard Rate, Exponential distribution, reliability approximation, engineering item.

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