Search results for: Nonlinear time series analysis

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

Abstract:

River flow prediction is an essential tool to ensure proper management of water resources and the optimal distribution of water to consumers. This study presents an analysis and prediction by using nonlinear prediction method with monthly river flow data for Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The reconstruction of phase space involves the reconstruction of one-dimension (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. The 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) was employed to compare prediction performance for the nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show that the prediction results using the nonlinear prediction method are better than ARIMA and SVM. Therefore, the results of this study could be used to develop an efficient water management system to optimize the allocation of water resources.

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

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Authors: Asar Khan, Peter D. Widdop, Andrew J. Day, Aliaster S. Wood, Steve, R. Mounce, John Machell

Abstract:

This paper describes an automated event detection and location system for water distribution pipelines which is based upon low-cost sensor technology and signature analysis by an Artificial Neural Network (ANN). The development of a low cost failure sensor which measures the opacity or cloudiness of the local water flow has been designed, developed and validated, and an ANN based system is then described which uses time series data produced by sensors to construct an empirical model for time series prediction and classification of events. These two components have been installed, tested and verified in an experimental site in a UK water distribution system. Verification of the system has been achieved from a series of simulated burst trials which have provided real data sets. It is concluded that the system has potential in water distribution network management.

Keywords: Detection, leakage, neural networks, sensors, water distribution networks

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Authors: Jafar Biazar, Behzad Ghanbari

Abstract:

In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

Keywords: System of nonlinear equations.

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Authors: Nizami Mustafa, C. Ardil

Abstract:

In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

Keywords: Approximate solution, Fixed-point principle, Nonlinear singular integral equations, Vekua integral operator

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Authors: Insung Jung, lockjo Koo, Gi-Nam Wang

Abstract:

The objective of this paper is to design a model of human vital sign prediction for decreasing prediction error by using two states mapping based time series neural network BP (back-propagation) model. Normally, lot of industries has been applying the neural network model by training them in a supervised manner with the error back-propagation algorithm for time series prediction systems. However, it still has a residual error between real value and prediction output. Therefore, we designed two states of neural network model for compensation of residual error which is possible to use in the prevention of sudden death and metabolic syndrome disease such as hypertension disease and obesity. We found that most of simulations cases were satisfied by the two states mapping based time series prediction model compared to normal BP. In particular, small sample size of times series were more accurate than the standard MLP model. We expect that this algorithm can be available to sudden death prevention and monitoring AGENT system in a ubiquitous homecare environment.

Keywords: Neural network, U-healthcare, prediction, timeseries, computer aided prediction.

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Authors: Fouad Salha , X. Guillaud

Abstract:

Directional over current relays (DOCR) are commonly used in power system protection as a primary protection in distribution and sub-transmission electrical systems and as a secondary protection in transmission systems. Coordination of protective relays is necessary to obtain selective tripping. In this paper, an approach for efficiency reduction of DOCRs nonlinear optimum coordination (OC) is proposed. This was achieved by modifying the objective function and relaxing several constraints depending on the four constraints classification, non-valid, redundant, pre-obtained and valid constraints. According to this classification, the far end fault effect on the objective function and constraints, and in consequently on relay operating time, was studied. The study was carried out, firstly by taking into account the near-end and far-end faults in DOCRs coordination problem formulation; and then faults very close to the primary relays (nearend faults). The optimal coordination (OC) was achieved by simultaneously optimizing all variables (TDS and Ip) in nonlinear environment by using of Genetic algorithm nonlinear programming techniques. The results application of the above two approaches on 6-bus and 26-bus system verify that the far-end faults consideration on OC problem formulation don-t lose the optimality.

Keywords: Backup/Primary relay, Coordination time interval (CTI), directional over current relays, Genetic algorithm, time dial setting (TDS), pickup current setting (Ip), nonlinear programming.

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Authors: R. Mechgoug, A. Titaouine

Abstract:

Fuzzy systems have been successfully used for exchange rate forecasting. However, fuzzy system is very confusing and complex to be designed by an expert, as there is a large set of parameters (fuzzy knowledge base) that must be selected, it is not a simple task to select the appropriate fuzzy knowledge base for an exchange rate forecasting. The researchers often look the effect of fuzzy knowledge base on the performances of fuzzy system forecasting. This paper proposes a genetic fuzzy predictor to forecast the future value of daily US Dollar/Euro exchange rate time’s series. A range of methodologies based on a set of fuzzy predictor’s which allow the forecasting of the same time series, but with a different fuzzy partition. Each fuzzy predictor is built from two stages, where each stage is performed by a real genetic algorithm.

Keywords: Foreign exchange rate, time series forecasting, Fuzzy System, and Genetic Algorithm.

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Authors: Janak Raj Sharma, Rajni Sharma

Abstract:

Based on Traub-s methods for solving nonlinear equation f(x) = 0, we develop two families of third-order methods for solving system of nonlinear equations F(x) = 0. The families include well-known existing methods as special cases. The stability is corroborated by numerical results. Comparison with well-known methods shows that the present methods are robust. These higher order methods may be very useful in the numerical applications requiring high precision in their computations because these methods yield a clear reduction in number of iterations.

Keywords: Nonlinear equations and systems, Newton's method, fixed point iteration, order of convergence.

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Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

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This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: State estimation, control systems, observer systems, unscented Kalman filter, nonlinear vehicle dynamics.

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Authors: Katleho D. Makatjane, Kalebe M. Kalebe

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The present paper used time-varying parameters which are based on the score function of a probability density at time t to model volatility of saving rate. We used a scaled likelihood function to update the parameters of the model overtime. Our results revealed high diligence of time-varying since the location parameter is greater than zero. Furthermore, we discovered a leptokurtic condition on saving rate’s distribution. Kapetanios, Shin-Shell Nonlinear Augmented Dickey-Fuller (KSS-NADF) test showed that the saving rate has a nonlinear unit root; therefore, it can be modeled by a generalised autoregressive score (GAS) model. Additionally, value at risk (VaR) and conditional tail expectation (CTE) indicate that 99% of the time people in Lesotho are saving more than spending. This puts the economy in high risk of not expanding. Therefore, the monetary policy committee (MPC) of Lesotho should revise their monetary policies towards this high saving rates risk.

Keywords: Generalized autoregressive score, time-varying, saving rate, Lesotho.

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Authors: Farzan Namvari, Panam Zarfam

Abstract:

Nowadays use of a new structural bracing system called 'Knee Bracing System' have taken the specialists attention too much. On the other hand nonlinear static analysis procedures in estimate structures performance in earthquake time have taken attention too much. One of these procedure is modal pushover analysis (MPA) procedure. The accuracy of MPA procedure for simple steel moment resisting frame has been verified and considered in Chintanapakdee and Chopra-s article in 2003. Since the accuracy of MPA procedure has not verified for semi-rigid steel frames with knee bracing, we are going to get through with this matter in this study. For this purpose, the selected structures are four frames with different heights, 5 to 20 stories, will be designed according to AISC criteria. Then MPA procedure is used for the same frames with different rigidity percentiles of connections. The results of seismic responses are compared with dynamic nonlinear response history analysis as exact procedure and accuracy of MPA procedure is evaluated. It seems that MPA procedure accuracy will come down by reduction of the rigidity percentiles of semi-rigid connections.

Keywords: Knee Bracing, Modal Pushover Analysis, SeismicBehavior, Semi-Rigid Connections.

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

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The objective of this paper is to compare the time specification performance between conventional controller PID and modern controller SMC for an inverted pendulum system. The goal is to determine which control strategy delivers better performance with respect to pendulum-s angle and cart-s position. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. Two controllers are presented such as Sliding Mode Control (SMC) and Proportional- Integral-Derivatives (PID) controllers for controlling the highly nonlinear system of inverted pendulum model. Simulation study has been done in Matlab Mfile and simulink environment shows that both controllers are capable to control multi output inverted pendulum system successfully. The result shows that Sliding Mode Control (SMC) produced better response compared to PID control strategies and the responses are presented in time domain with the details analysis.

Keywords: SMC, PID, Inverted Pendulum System.

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Authors: Yuki. Akiyama, Hiroaki. Sengoku, Ryosuke. Shibasaki

Abstract:

In this study, the locations and areas of commercial accumulations were detected by using digital yellow page data. An original buffering method that can accurately create polygons of commercial accumulations is proposed in this paper.; by using this method, distribution of commercial accumulations can be easily created and monitored over a wide area. The locations, areas, and time-series changes of commercial accumulations in the South Kanto region can be monitored by integrating polygons of commercial accumulations with the time-series data of digital yellow page data. The circumstances of commercial accumulations were shown to vary according to areas, that is, highly- urbanized regions such as the city center of Tokyo and prefectural capitals, suburban areas near large cities, and suburban and rural areas.

Keywords: Commercial accumulations, Spatio-temporal analysis, Urban monitoring, Yellow page data

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Authors: Cameron Hamilton, Walter Potter, Gerrit Hoogenboom, Ronald McClendon, Will Hobbs

Abstract:

A model was constructed to predict the amount of solar radiation that will make contact with the surface of the earth in a given location an hour into the future. This project was supported by the Southern Company to determine at what specific times during a given day of the year solar panels could be relied upon to produce energy in sufficient quantities. Due to their ability as universal function approximators, an artificial neural network was used to estimate the nonlinear pattern of solar radiation, which utilized measurements of weather conditions collected at the Griffin, Georgia weather station as inputs. A number of network configurations and training strategies were utilized, though a multilayer perceptron with a variety of hidden nodes trained with the resilient propagation algorithm consistently yielded the most accurate predictions. In addition, a modeled direct normal irradiance field and adjacent weather station data were used to bolster prediction accuracy. In later trials, the solar radiation field was preprocessed with a discrete wavelet transform with the aim of removing noise from the measurements. The current model provides predictions of solar radiation with a mean square error of 0.0042, though ongoing efforts are being made to further improve the model’s accuracy.

Keywords: Artificial Neural Networks, Resilient Propagation, Solar Radiation, Time Series Forecasting.

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Authors: Antoni Wibowo, Harry Pujianto, Dewi Retno Sari Saputro

Abstract:

The stock market can provide huge profits in a relatively short time in financial sector; however, it also has a high risk for investors and traders if they are not careful to look the factors that affect the stock market. Therefore, they should give attention to the dynamic fluctuations and movements of the stock market to optimize profits from their investment. In this paper, we present a nonlinear autoregressive exogenous model (NARX) to predict the movements of stock market; especially, the movements of the closing price index. As case study, we consider to predict the movement of the closing price in Indonesia composite index (IHSG) and choose the best structures of NARX for IHSG’s prediction.

Keywords: NARX, prediction, stock market, time series.

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Authors: Ramin Vafadary, Maryam Khanbaghi

Abstract:

Forecasting electricity load is important for various purposes like planning, operation and control. Forecasts can save operating and maintenance costs, increase the reliability of power supply and delivery systems, and correct decisions for future development. This paper compares various time series methods to forecast 24 hours ahead of electricity load. The methods considered are the Holt-Winters smoothing, SARIMA Modeling, LSTM Network, Fbprophet and Tensorflow probability. The performance of each method is evaluated by using the forecasting accuracy criteria namely, the Mean Absolute Error and Root Mean Square Error. The National Renewable Energy Laboratory (NREL) residential energy consumption data are used to train the models. The results of this study show that SARIMA model is superior to the others for 24 hours ahead forecasts. Furthermore, a Bagging technique is used to make the predictions more robust. The obtained results show that by Bagging multiple time-series forecasts we can improve the robustness of the models for 24 hour ahead electricity load forecasting.

Keywords: Bagging, Fbprophet, Holt-Winters, LSTM, Load Forecast, SARIMA, tensorflow probability, time series.

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Authors: A. Keshavarz, Z. Roosta

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In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: Paraxial group transformation, nonlocal nonlinear media, Cos-Gaussian beam, ABCD law.

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Authors: Kunya Bowornchockchai

Abstract:

The objective of this research is to forecast the monthly exchange rate between Thai baht and the US dollar and to compare two forecasting methods. The methods are Box-Jenkins’ method and Holt’s method. Results show that the Box-Jenkins’ method is the most suitable method for the monthly Exchange Rate between Thai Baht and the US Dollar. The suitable forecasting model is ARIMA (1,1,0)  without constant and the forecasting equation is Y_t = Y_t-1 + 0.3691 (Y_t-1 - Y_t-2) When Y_t  is the time series data at time t, respectively.

Keywords: Box–Jenkins Method, Holt’s Method, Mean Absolute Percentage Error (MAPE).

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Authors: C. C. Wang, N. S. Pai, H. T. Yau, T. T. Liao, M. J. Jang, C. W. Lee, W. M. Hong

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Horizontal platform system (HPS) is popularly applied in offshore and earthquake technology, but it is difficult and time-consuming for regulation. In order to understand the nonlinear dynamic behavior of HPS and reduce the cost when using it, this paper employs differential transformation method to study the bifurcation behavior of HPS. The numerical results reveal a complex dynamic behavior comprising periodic, sub-harmonic, and chaotic responses. Furthermore, the results reveal the changes which take place in the dynamic behavior of the HPS as the external torque is increased. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of horizontal platform system.

Keywords: horizontal platform system, differentialtransformation method, chaotic.

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Authors: B. S. Saini, Dilbag Singh, Moin Uddin, Vinod Kumar

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The RR interval series is non-stationary and unevenly spaced in time. For estimating its power spectral density (PSD) using traditional techniques like FFT, require resampling at uniform intervals. The researchers have used different interpolation techniques as resampling methods. All these resampling methods introduce the low pass filtering effect in the power spectrum. The lomb transform is a means of obtaining PSD estimates directly from irregularly sampled RR interval series, thus avoiding resampling. In this work, the superiority of Lomb transform method has been established over FFT based approach, after applying linear and cubicspline interpolation as resampling methods, in terms of reproduction of exact frequency locations as well as the relative magnitudes of each spectral component.

Keywords: HRV, Lomb Transform, Resampling, RR-intervals.

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Authors: Swarniv Chandra, Basudev Ghosh

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Nonlinear solitary structures of electron plasma waves have been investigated by using nonlinear quantum fluid equations for electrons with an arbitrary temperature. It is shown that the electron degeneracy parameter has significant effects on the linear and nonlinear properties of electron plasma waves. Depending on its value both compressive and rarefactive solitons can be excited in the model plasma under consideration.

Keywords: Electron Plasma Waves, Finite Temperature Model, Modulational Instability, Quantum Plasma, Solitary structure

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Authors: P.-W. Tsai, C.-Y. Chen, C.-W. Chen

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In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Keywords: Adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm.

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Authors: Jimeng Shi, Mahek Jain, Giri Narasimhan

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Time Series Forecasting (TSF) is used to predict the target variables at a future time point based on the learning from previous time points. To keep the problem tractable, learning methods use data from a fixed length window in the past as an explicit input. In this paper, we study how the performance of predictive models change as a function of different look-back window sizes and different amounts of time to predict into the future. We also consider the performance of the recent attention-based transformer models, which had good success in the image processing and natural language processing domains. In all, we compare four different deep learning methods (Recurrent Neural Network (RNN), Long Short-term Memory (LSTM), Gated Recurrent Units (GRU), and Transformer) along with a baseline method. The dataset (hourly) we used is the Beijing Air Quality Dataset from the website of University of California, Irvine (UCI), which includes a multivariate time series of many factors measured on an hourly basis for a period of 5 years (2010-14). For each model, we also report on the relationship between the performance and the look-back window sizes and the number of predicted time points into the future. Our experiments suggest that Transformer models have the best performance with the lowest Mean   Absolute Errors (MAE = 14.599, 23.273) and Root Mean Square Errors (RSME = 23.573, 38.131) for most of our single-step and multi-steps predictions. The best size for the look-back window to predict 1 hour into the future appears to be one day, while 2 or 4 days perform the best to predict 3 hours into the future.

Keywords: Air quality prediction, deep learning algorithms, time series forecasting, look-back window.

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Authors: Sagaren Pillay

Abstract:

In this paper bi-annual time series data on unemployment rates (from the Labour Force Survey) are expanded to quarterly rates and linked to quarterly unemployment rates (from the Quarterly Labour Force Survey). The resultant linked series and the consumer price index (CPI) series are examined using Johansen’s cointegration approach and vector error correction modeling. The study finds that both the series are integrated of order one and are cointegrated. A statistically significant co-integrating relationship is found to exist between the time series of unemployment rates and the CPI. Given this significant relationship, the study models this relationship using Vector Error Correction Models (VECM), one with a restriction on the deterministic term and the other with no restriction.

A formal statistical confirmation of the existence of a unique linear and lagged relationship between inflation and unemployment for the period between September 2000 and June 2011 is presented. For the given period, the CPI was found to be an unbiased predictor of the unemployment rate. This relationship can be explored further for the development of appropriate forecasting models incorporating other study variables.

Keywords: Forecasting, lagged, linear, relationship.

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Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid.

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Authors: T. Sanches, K. Bousson

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As part of the development of a 4D autopilot system for unmanned aerial vehicles (UAVs), i.e. a time-dependent robust trajectory generation and control algorithm, this work addresses the problem of optimal path control based on the flight sensors data output that may be unreliable due to noise on data acquisition and/or transmission under certain circumstances. Although several filtering methods, such as the Kalman-Bucy filter or the Linear Quadratic Gaussian/Loop Transfer Recover Control (LQG/LTR), are available, the utter complexity of the control system, together with the robustness and reliability required of such a system on a UAV for airworthiness certifiable autonomous flight, required the development of a proper robust filter for a nonlinear system, as a way of further mitigate errors propagation to the control system and improve its ,performance. As such, a nonlinear algorithm based upon the LQG/LTR, is validated through computational simulation testing, is proposed on this paper.

Keywords: Autonomous flight, LQG/LTR, nonlinear state estimator, robust flight control and stability.

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Authors: Rafael Jorge Menezes Santos, Ginalber Luiz de Oliveira Serra, Carlos César Teixeira Ferreira

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This paper proposes a methodology for analysis of the dynamic behavior of a robotic manipulator in continuous time. Initially this system (nonlinear system) will be decomposed into linear submodels and analyzed in the context of the Linear and Parameter Varying (LPV) Systems. The obtained linear submodels, which represent the local dynamic behavior of the robotic manipulator in some operating points were grouped in a Takagi-Sugeno fuzzy structure. The obtained fuzzy model was analyzed and validated through analog simulation, as universal approximator of the robotic manipulator.

Keywords: modeling of nonlinear dynamic systems, Takagi- Sugeno fuzzy model, Linear and Parameter Varying (LPV) System.

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Authors: Rajoo Pandey

Abstract:

Most of the commonly used blind equalization algorithms are based on the minimization of a nonconvex and nonlinear cost function and a neural network gives smaller residual error as compared to a linear structure. The efficacy of complex valued feedforward neural networks for blind equalization of linear and nonlinear communication channels has been confirmed by many studies. In this paper we present two neural network models for blind equalization of time-varying channels, for M-ary QAM and PSK signals. The complex valued activation functions, suitable for these signal constellations in time-varying environment, are introduced and the learning algorithms based on the CMA cost function are derived. The improved performance of the proposed models is confirmed through computer simulations.

Keywords: Blind Equalization, Neural Networks, Constant Modulus Algorithm, Time-varying channels.

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Authors: Snezhana G. Gocheva-Ilieva, Ivan H. Feschiev

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In this study integral form and new recursive formulas for Favard constants and some connected with them numeric and Fourier series are obtained. The method is based on preliminary integration of Fourier series which allows for establishing finite recursive representations for the summation. It is shown that the derived recursive representations are numerically more effective than known representations of the considered objects.

Keywords: Effective summation of series, Favard constants, finite recursive representations, Fourier series

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Authors: K. Karuppasamy

Abstract:

In this paper, analysis of an infinite beam resting on multilayer tensionless extensible geosynthetic reinforced granular fill-poor soil system overlying soft soil strata under moving load with constant velocity is presented. The beam is subjected to a concentrated load moving with constant velocity. The upper reinforced granular bed is modeled by a rough membrane embedded in Pasternak shear layer overlying a series of compressible nonlinear winkler springs representing the underlying the very poor soil. The multilayer tensionless extensible geosynthetic layer has been assumed to deform such that at interface the geosynthetic and the soil have some deformation. Nonlinear behaviour of granular fill and the very poor soil has been considered in the analysis by means of hyperbolic constitutive relationships. Governing differential equations of the soil foundation system have been obtained and solved with the help of appropriate boundary conditions. The solution has been obtained by employing finite difference method by means of Gauss-Siedal iterative scheme. Detailed parametric study has been conducted to study the influence of various parameters on the response of soil–foundation system under consideration by means of deflection and bending moment in the beam and tension mobilized in the geosynthetic layer. These parameters include magnitude of applied load, velocity of load, damping, ultimate resistance of poor soil and granular fill layer. Range of values of parameters has been considered as per Indian Railway conditions. This study clearly observed that the comparisons of multilayer tensionless extensible geosynthetic reinforcement with poor foundation soil and magnitude of applied load, relative compressibility of granular fill and ultimate resistance of poor soil has significant influence on the response of soil–foundation system.

Keywords: Infinite beams, multilayer tensionless extensible geosynthetic, granular layer, moving load, nonlinear behavior of poor soil.

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