Search results for: Linear Eigenvalue analysis

Authors: M. A. Sadeghian, J. Yang, Q. F. Liu

Abstract:

Steel extended end plate bolted connections are recommended to be widely utilized in special moment-resisting frame subjected to monotonic loading. Improper design of steel beam to column connection can lead to the collapse and fatality of structures. Therefore comprehensive research studies of beam to column connection design should be carried out. Also the performance and effect of corrugated on the strength of beam column end plate connection up to failure under monotonic loading in horizontal direction is presented in this paper. The non-linear elastic–plastic behavior has been considered through a finite element analysis using the multi-purpose software package LUSAS. The effect of vertically and horizontally types of corrugated web was also investigated.

Keywords: Corrugated beam, monotonic loading, finite element analysis, end plate connection.

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Authors: Sung Wook Yun, Yun Jong Choi, Kyong-min Lee, Poogyeon Park*

Abstract:

Repetitive systems stand for a kind of systems that perform a simple task on a fixed pattern repetitively, which are widely spread in industrial fields. Hence, many researchers have been interested in those systems, especially in the field of iterative learning control (ILC). In this paper, we propose a finite-horizon tracking control scheme for linear time-varying repetitive systems with uncertain initial conditions. The scheme is derived both analytically and numerically for state-feedback systems and only numerically for output-feedback systems. Then, it is extended to stable systems with input constraints. All numerical schemes are developed in the forms of linear matrix inequalities (LMIs). A distinguished feature of the proposed scheme from the existing iterative learning control is that the scheme guarantees the tracking performance exactly even under uncertain initial conditions. The simulation results demonstrate the good performance of the proposed scheme.

Keywords: Finite time horizon, linear matrix inequality (LMI), repetitive system, uncertain initial condition.

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Authors: Li Jiang, Baoguang Tian

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In this paper, we present the preconditioned mixed-type splitting iterative method for solving the linear systems, Ax = b, where A is a Z-matrix. And we give some comparison theorems to show that the convergence rate of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give a numerical example to illustrate our results.

Keywords: Z-matrix, mixed-type splitting iterative method, precondition, comparison theorem, linear system.

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Authors: Ming-Tsang Wu

Abstract:

The purpose of this study was to explore the correlation between leisure participation and perceived wellness, with the students of a nursing college in southern Taiwan as the subjects. One thousand six hundred and ninety-six (1,696) surveys were sent, and 1,408 surveys were received for an 83.02% valid response rate. Using canonical correlation analysis to analyze the data, the results showed that the linear combination of the two sets of variable produces five significant canonical variates. Out of the five canonical variates, only the first has sufficient explanatory power. The canonical correlation coefficient of first canonical variate is 0.660. This indicated that leisure participation and perceived wellness are significantly correlated.

Keywords: Leisure, perceived wellness.

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Authors: L. Basha, E. Gjika

Abstract:

This study is focused on analyzing climate change in Albania and its potential effects on cereal yields. Initially, monthly temperature and rainfalls in Albania were studied for the period 1960-2021. Climacteric variables are important variables when trying to model cereal yield behavior, especially when significant changes in weather conditions are observed. For this purpose, in the second part of the study, linear and nonlinear models explaining cereal yield are constructed for the same period, 1960-2021. The multiple linear regression analysis and lasso regression method are applied to the data between cereal yield and each independent variable: average temperature, average rainfall, fertilizer consumption, arable land, land under cereal production, and nitrous oxide emissions. In our regression model, heteroscedasticity is not observed, data follow a normal distribution, and there is a low correlation between factors, so we do not have the problem of multicollinearity. Machine learning methods, such as Random Forest (RF), are used to predict cereal yield responses to climacteric and other variables. RF showed high accuracy compared to the other statistical models in the prediction of cereal yield. We found that changes in average temperature negatively affect cereal yield. The coefficients of fertilizer consumption, arable land, and land under cereal production are positively affecting production. Our results show that the RF method is an effective and versatile machine-learning method for cereal yield prediction compared to the other two methods: multiple linear regression and lasso regression method.

Keywords: Cereal yield, climate change, machine learning, multiple regression model, random forest.

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Authors: Jan-Tore H. Horn, Jørgen Juncher Jensen

Abstract:

Uncertainties related to fatigue damage estimation of non-linear systems are highly dependent on the tail behaviour and extreme values of the stress range distribution. By using a combination of the First Order Reliability Method (FORM) and Monte Carlo simulations (MCS), the accuracy of the fatigue estimations may be improved for the same computational efforts. The method is applied to a bottom-fixed, monopile-supported large offshore wind turbine, which is a non-linear and dynamically sensitive system. Different curve fitting techniques to the fatigue damage distribution have been used depending on the sea-state dependent response characteristics, and the effect of a bi-linear S-N curve is discussed. Finally, analyses are performed on several environmental conditions to investigate the long-term applicability of this multistep method. Wave loads are calculated using state-of-the-art theory, while wind loads are applied with a simplified model based on rotor thrust coefficients.

Keywords: Fatigue damage, FORM, monopile, monte carlo simulation, reliability, wind turbine.

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Authors: Safae El Alaoui, Mohamed Ouzahra

Abstract:

In this work, we investigate the exponential stability of a linear system described by x˙ (t) = Ax(t) − ρBx(t). Here, A generates a semigroup S(t) on a Hilbert space, the operator B is supposed to be of Desch-Schappacher type, which makes the investigation more interesting in many applications. The case of Miyadera-Voigt perturbations is also considered. Sufficient conditions are formulated in terms of admissibility and observability inequalities and the approach is based on some energy estimates. Finally, the obtained results are applied to prove the uniform exponential stabilization of bilinear partial differential equations.

Keywords: Exponential stabilization, unbounded operator, Desch-Schappacher, Miyadera-Voigt operator.

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Authors: Ahmed E. Hodaib, Samar F. Abdel Fattah

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High-speed transportation is a growing concern. To develop high-speed rails and to increase high-speed efficiencies, the idea of Hyperloop was introduced. The challenge is to overcome the difficulties of managing friction and air-resistance which become substantial when vehicles approach high speeds. In this paper, we are presenting the methodologies of the capsule design which got a design concept innovation award at SpaceX competition in January, 2016. MATLAB scripts are written for the levitation and propulsion calculations and iterations. Computational Fluid Dynamics (CFD) is used to simulate the air flow around the capsule considering the effect of the axial-flow air compressor and the levitation cushion on the air flow. The design procedures of a single-sided linear induction motor are analyzed in detail and its geometric and magnetic parameters are determined. A structural design is introduced and Finite Element Method (FEM) is used to analyze the stresses in different parts. The configuration and the arrangement of the components are illustrated. Moreover, comments on manufacturing are made.

Keywords: High-speed transportation, Hyperloop, railways transportation, single-sided linear induction motor.

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Authors: A.H. Akhaveissy

Abstract:

Nonlinear finite element method and Serendipity eight nodes element are used for determining of ground surface settlement due to tunneling. Linear element with elastic behavior is used for modeling of lining. Modified Generalized plasticity model with nonassociated flow rule is applied for analysis of a tunnel in Sao Paulo – Brazil. The tunnel had analyzed by Lades- model with 16 parameters. In this work modified Generalized Plasticity is used with 10 parameters, also Mohr-Coulomb model is used to analysis the tunnel. The results show good agreement with observed results of field data by modified Generalized Plasticity model than other models. The obtained result by Mohr-Coulomb model shows less settlement than other model due to excavation.

Keywords: Non-associated flow rule, Generalized plasticity, tunnel excavation, Excavation method.

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Authors: S. T. Tan, H. Hashim, W. S. Ho, C. T. Lee

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Rapid economic development and population growth in Malaysia had accelerated the generation of solid waste. This issue gives pressure for effective management of municipal solid waste (MSW) to take place in Malaysia due to the increased cost of landfill. This paper discusses optimal planning of waste-to-energy (WTE) using a combinatorial simulation and optimization model through mixed integer linear programming (MILP) approach. The proposed multi-period model is tested in Iskandar Malaysia (IM) as case study for a period of 12 years (2011 -2025) to illustrate the economic potential and tradeoffs involved in this study. In this paper, 3 scenarios have been used to demonstrate the applicability of the model: (1) Incineration scenario (2) Landfill scenario (3) Optimal scenario. The model revealed that the minimum cost of electricity generation from 9,995,855 tonnes of MSW is estimated as USD 387million with a total electricity generation of 50MW /yr in the optimal scenario.

Keywords: Mixed Integer Linear Programming (MILP), optimization, solid waste management (SWM), Waste-to-energy (WTE).

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Authors: M. Analoui, M. Fadavi Amiri

Abstract:

The design of a pattern classifier includes an attempt to select, among a set of possible features, a minimum subset of weakly correlated features that better discriminate the pattern classes. This is usually a difficult task in practice, normally requiring the application of heuristic knowledge about the specific problem domain. The selection and quality of the features representing each pattern have a considerable bearing on the success of subsequent pattern classification. Feature extraction is the process of deriving new features from the original features in order to reduce the cost of feature measurement, increase classifier efficiency, and allow higher classification accuracy. Many current feature extraction techniques involve linear transformations of the original pattern vectors to new vectors of lower dimensionality. While this is useful for data visualization and increasing classification efficiency, it does not necessarily reduce the number of features that must be measured since each new feature may be a linear combination of all of the features in the original pattern vector. In this paper a new approach is presented to feature extraction in which feature selection, feature extraction, and classifier training are performed simultaneously using a genetic algorithm. In this approach each feature value is first normalized by a linear equation, then scaled by the associated weight prior to training, testing, and classification. A knn classifier is used to evaluate each set of feature weights. The genetic algorithm optimizes a vector of feature weights, which are used to scale the individual features in the original pattern vectors in either a linear or a nonlinear fashion. By this approach, the number of features used in classifying can be finely reduced.

Keywords: Feature reduction, genetic algorithm, pattern classification, nearest neighbor rule classifiers (k-NNR).

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Authors: G. C. Mahata, A. Goswami

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This paper deals with infinite time horizon fuzzy Economic Order Quantity (EOQ) models for deteriorating items with  stock dependent demand rate and nonlinear holding costs by taking deterioration rate θ0 as a triangular fuzzy number  (θ0 −δ 1, θ0, θ0 +δ 2), where 1 2 0 0 <δ ,δ <θ are fixed real numbers. The traditional parameters such as unit cost and ordering  cost have been kept constant but holding cost is considered to vary. Two possibilities of variations in the holding cost function namely, a non-linear function of the length of time for which the item is held in stock and a non-linear function of the amount of on-hand inventory have been used in the models. The approximate optimal solution for the fuzzy cost functions in both these cases have been obtained and the effect of non-linearity in holding costs is studied with the help of a numerical example.

Keywords: Inventory Model, Deterioration, Holding Cost, Fuzzy Total Cost, Extension Principle.

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of exponential stability analysis for recurrent neural networks with time-varying delay.By establishing a suitable augmented LyapunovCKrasovskii function and a novel sufficient condition is obtained to guarantee the exponential stability of the considered system.In order to get a less conservative results of the condition,zero equalities and reciprocally convex approach are employed. The several exponential stability criterion proposed in this paper is simpler and effective. A numerical example is provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Exponential stability , Neural networks, Linear matrix inequality, Lyapunov-Krasovskii, Time-varying.

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Authors: Ali Ameur Haj Salah, Tarek Garna, Hassani Messaoud

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This paper attempts to define the validity domain of LSDP (Loop Shaping Design Procedure) controller system, by determining the suitable uncertainty region, so that linear system be stable. Indeed the LSDP controller cannot provide stability for any perturbed system. For this, we will use the gap metric tool that is introduced into the control literature for studying robustness properties of feedback systems with uncertainty. A 2nd order electric linear system example is given to define the validity domain of LSDP controller and effectiveness gap metric.

Keywords: LSDP, Gap metric, Robust Control.

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Authors: Abdel-Aziz M. Mohamed, Nermeen Coutry

Abstract:

Lead time is a critical measure of a supply chain's performance. It impacts both the customer satisfactions as well as the total cost of inventory. This paper presents the result of a study on the analysis of the customer order lead-time for a multinational company. In the study, the lead time was divided into three stages respectively: order entry, order fulfillment, and order delivery. A sample of size 2,425 order lines was extracted from the company's records to use for this study. The sample data entails information regarding customer orders from the time of order entry until order delivery. Data regarding the lead time of each stage for different orders were also provided. Summary statistics on lead time data reveals that about 30% of the orders were delivered later than the scheduled due date. The result of the multiple linear regression analysis technique revealed that component type, logistics parameter, order size and the customer type have significant impacts on lead time. Data analysis on the stages of lead time indicates that stage 2 consumed over 50% of the lead time. Pareto analysis was made to study the reasons for the customer order delay in each stage. Recommendation was given to resolve the problem.

Keywords: Lead time reduction, customer satisfaction, service quality, statistical analysis.

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Authors: Radouane Iqdour, Abdelouhab Zeroual

Abstract:

The Multi-Layered Perceptron (MLP) Neural networks have been very successful in a number of signal processing applications. In this work we have studied the possibilities and the met difficulties in the application of the MLP neural networks for the prediction of daily solar radiation data. We have used the Polack-Ribière algorithm for training the neural networks. A comparison, in term of the statistical indicators, with a linear model most used in literature, is also performed, and the obtained results show that the neural networks are more efficient and gave the best results.

Keywords: Daily solar radiation, Prediction, MLP neural networks, linear model

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Authors: H. D. Ibrahim, H. C. Chinwenyi, H. N. Ude

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In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, Gauss-Seidel, Jacobi, algorithm

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Authors: Nader H. Ghareeb, Mohamed S. Gaith, Sayed M. Soleimani

Abstract:

In modern engineering, weight optimization has a priority during the design of structures. However, optimizing the weight can result in lower stiffness and less internal damping, causing the structure to become excessively prone to vibration. To overcome this problem, active or smart materials are implemented. The coupled electromechanical properties of smart materials, used in the form of piezoelectric ceramics in this work, make these materials well-suited for being implemented as distributed sensors and actuators to control the structural response. The smart structure proposed in this paper is composed of a cantilevered steel beam, an adhesive or bonding layer, and a piezoelectric actuator. The static deflection of the structure is derived as function of the piezoelectric voltage, and the outcome is compared to theoretical and experimental results from literature. The relation between the voltage and the piezoelectric moment at both ends of the actuator is also investigated and a reduced finite element model of the smart structure is created and verified. Finally, a linear controller is implemented and its ability to attenuate the vibration due to the first natural frequency is demonstrated.

Keywords: Active linear control, Lyapunov stability theorem, piezoelectricity, smart structure, static deflection.

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Authors: Ram Kumar Soni, Alok Jain, Rajiv Saxena

Abstract:

This paper proposes an efficient method for the design of two channel quadrature mirror filter (QMF) bank. To achieve minimum value of reconstruction error near to perfect reconstruction, a linear optimization process has been proposed. Prototype low pass filter has been designed using Kaiser window function. The modified algorithm has been developed to optimize the reconstruction error using linear objective function through iteration method. The result obtained, show that the performance of the proposed algorithm is better than that of the already exists methods.

Keywords: Filterbank, near perfect reconstruction, Kaiserwindow, QMF.

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Authors: Saber Saati Mohtadi, Ali Payan, Azizallah Kord

Abstract:

One of the most important issues in multi-criteria decision analysis (MCDA) is to determine the weights of criteria so that all alternatives can be compared based on the collective performance of criteria. In this paper, one of popular methods in data envelopment analysis (DEA) known as common weights (CWs) is used to determine the weights in MCDA. Two frontiers named ideal and anti-ideal frontiers, instead of ideal and anti-ideal alternatives, are defined based on two new proposed CWs models. Ideal and antiideal frontiers are more flexible than that of alternatives. According to the optimal solutions of these two models, the distances of an alternative from the ideal and anti-ideal frontiers are derived. Then, a relative distance is introduced to measure the value of each alternative. The suggested models are linear and despite weight restrictions are feasible. An example is presented for explaining the method and for comparing to the existing literature.

Keywords: Anti-ideal frontier, Common weights (CWs), Ideal frontier, Multi-criteria decision analysis (MCDA)

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Authors: Rajamani Doraiswami, Lahouari Cheded

Abstract:

Fault diagnosis of Linear Parameter-Varying (LPV) system using an adaptive Kalman filter is proposed. The LPV model is comprised of scheduling parameters, and the emulator parameters. The scheduling parameters are chosen such that they are capable of tracking variations in the system model as a result of changes in the operating regimes. The emulator parameters, on the other hand, simulate variations in the subsystems during the identification phase and have negligible effect during the operational phase. The nominal model and the influence vectors, which are the gradient of the feature vector respect to the emulator parameters, are identified off-line from a number of emulator parameter perturbed experiments. A Kalman filter is designed using the identified nominal model. As the system varies, the Kalman filter model is adapted using the scheduling variables. The residual is employed for fault diagnosis. The proposed scheme is successfully evaluated on simulated system as well as on a physical process control system.

Keywords: Keywords—Identification, linear parameter-varying systems, least-squares estimation, fault diagnosis, Kalman filter, emulators

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Authors: Meng-Hao Tsai, Tsuei-Chiang Huang

Abstract:

Interior brick-infill partitions are usually considered as non-structural components, and only their weight is accounted for in practical structural design. In this study, the brick-infill panels are simulated by compression struts to clarify their effect on the progressive collapse potential of an earthquake-resistant RC building. Three-dimensional finite element models are constructed for the RC building subjected to sudden column loss. Linear static analyses are conducted to investigate the variation of demand-to-capacity ratio (DCR) of beam-end moment and the axial force variation of the beams adjacent to the removed column. Study results indicate that the brick-infill effect depends on their location with respect to the removed column. As they are filled in a structural bay with a shorter span adjacent to the column-removed line, more significant reduction of DCR may be achieved. However, under certain conditions, the brick infill may increase the axial tension of the two-span beam bridging the removed column.

Keywords: Progressive collapse, brick-infill partition, compression strut.

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Authors: Ali Fellah Jahromi, Wen Fang Xie, Rama B. Bhat

Abstract:

A semi-active control strategy for suspension systems of passenger cars is presented employing Magnetorheological (MR) dampers. The vehicle is modeled with seven DOFs including the, roll pitch and bounce of car body, and the vertical motion of the four tires. In order to design an optimal controller based on the actuator constraints, a Linear-Quadratic Regulator (LQR) is designed. The design procedure of the LQR consists of selecting two weighting matrices to minimize the energy of the control system. This paper presents a hybrid optimization procedure which is a combination of gradient-based and evolutionary algorithms to choose the weighting matrices with regards to the actuator constraint. The optimization algorithm is defined based on maximum comfort and actuator constraints. It is noted that utilizing the present control algorithm may significantly reduce the vibration response of the passenger car, thus, providing a comfortable ride.

Keywords: Full car model, Linear Quadratic Regulator, Sequential Quadratic Programming, Genetic Algorithm

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Authors: Mehmet Bozca

Abstract:

Singular value decomposition based optimisation of geometric design parameters of a 5-speed gearbox is studied. During the optimisation, a four-degree-of freedom torsional vibration model of the pinion gear-wheel gear system is obtained and the minimum singular value of the transfer matrix is considered as the objective functions. The computational cost of the associated singular value problems is quite low for the objective function, because it is only necessary to compute the largest and smallest singular values (μmax and μmin) that can be achieved by using selective eigenvalue solvers; the other singular values are not needed. The design parameters are optimised under several constraints that include bending stress, contact stress and constant distance between gear centres. Thus, by optimising the geometric parameters of the gearbox such as, the module, number of teeth and face width it is possible to obtain a light-weight-gearbox structure. It is concluded that the all optimised geometric design parameters also satisfy all constraints.

Keywords: Singular value, optimisation, gearbox, torsional vibration.

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Authors: W. Wu, S. Utili

Abstract:

Based on the kinematic approach of limit analysis, a full set of upper bound solutions for the stability of homogeneous rock slopes subjected to tension cracks are obtained. The generalized Hoek-Brown failure criterion is employed to describe the non-linear strength envelope of rocks. In this paper, critical failure mechanisms are determined for cracks of known depth but unspecified location, cracks of known location but unknown depth, and cracks of unspecified location and depth. It is shown that there is a nearly up to 50% drop in terms of the stability factors for the rock slopes intersected by a tension crack compared with intact ones. Tables and charts of solutions in dimensionless forms are presented for ease of use by practitioners.

Keywords: Hoek-Brown failure criterion, limit analysis, rock slope, tension cracks.

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Authors: N. H. Adenan, M. S. M. Noorani

Abstract:

River flow prediction is an essential to ensure proper management of water resources can be optimally distribute water to consumers. This study presents an analysis and prediction by using nonlinear prediction method involving monthly river flow data in Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The phase space reconstruction involves the reconstruction of one-dimensional (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. Revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) have been employed to compare prediction performance for nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show the prediction results using nonlinear prediction method is better than ARIMA and SVM. Therefore, the result of this study could be used to develop an efficient water management system to optimize the allocation water resources.

Keywords: River flow, nonlinear prediction method, phase space, local linear approximation.

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Authors: Jiashan Tang

Abstract:

In this note, we investigate the blind source separability of linear FIR-MIMO systems. The concept of semi-reversibility of a system is presented. It is shown that for a semi-reversible system, if the input signals belong to a binary alphabet, then the source data can be blindly separated. One sufficient condition for a system to be semi-reversible is obtained. It is also shown that the proposed criteria is weaker than that in the literature which requires that the channel matrix is irreducible/invertible or reversible.

Keywords: Blind source separable, FIR-MIMO system, Binary input, Bezout equality.

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

In this paper, delay-dependent stability analysis for neutral type neural networks with uncertain paramters and time-varying delay is studied. By constructing new Lyapunov-Krasovskii functional and dividing the delay interval into multiple segments, a novel sufficient condition is established to guarantee the globally asymptotically stability of the considered system. Finally, a numerical example is provided to illustrate the usefulness of the proposed main results.

Keywords: Neutral type neural networks, Time-varying delay, Stability, Linear matrix inequality(LMI).

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Authors: Masoud Sadeghian, Alireza Fatehi

Abstract:

In this paper, we use nonlinear system identification method to predict and detect process fault of a cement rotary kiln. After selecting proper inputs and output, an input-output model is identified for the plant. To identify the various operation points in the kiln, Locally Linear Neuro-Fuzzy (LLNF) model is used. This model is trained by LOLIMOT algorithm which is an incremental treestructure algorithm. Then, by using this method, we obtained 3 distinct models for the normal and faulty situations in the kiln. One of the models is for normal condition of the kiln with 15 minutes prediction horizon. The other two models are for the two faulty situations in the kiln with 7 minutes prediction horizon are presented. At the end, we detect these faults in validation data. The data collected from White Saveh Cement Company is used for in this study.

Keywords: Cement Rotary Kiln, Fault Detection, Delay Estimation Method, Locally Linear Neuro Fuzzy Model, LOLIMOT.

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Authors: Kaushalendra K. Khadanga, Lee Hee Hyol

Abstract:

Passenger comfort has been paramount in the design of suspension systems of high speed cars. To analyze the effect of vibration on vehicle ride quality, a vertical model of a six degree of freedom railway passenger vehicle, with front and rear suspension, is built. It includes car body flexible effects and vertical rigid modes. A second order linear shaping filter is constructed to model Gaussian white noise into random rail excitation. The temporal correlation between the front and rear wheels is given by a second order Pade approximation. The complete track and the vehicle model are then designed. An active secondary suspension system based on a Linear Quadratic Gaussian (LQG) optimal control method is designed. The results show that the LQG control method reduces the vertical acceleration, pitching acceleration and vertical bending vibration of the car body as compared to the passive system.

Keywords: Active suspension, bending vibration, railway vehicle, vibration control.

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