The strategy of building a flood forecast model by neuro‐fuzzy network

A methodology is proposed for constructing a flood forecast model using the adaptive neuro‐fuzzy inference system (ANFIS). This is based on a self‐organizing rule‐base generator, a feedforward network, and fuzzy control arithmetic. Given the rainfall‐runoff patterns, ANFIS could systematically and effectively construct flood forecast models. The precipitation and flow data sets of the Choshui River in central Taiwan are analysed to identify the useful input variables and then the forecasting model can be self‐constructed through ANFIS. The analysis results suggest that the persistent effect and upstream flow information are the key effects for modelling the flood forecast, and the watershed's average rainfall provides further information and enhances the accuracy of the model performance. For the purpose of comparison, the commonly used back‐propagation neural network (BPNN) is also examined. The forecast results demonstrate that ANFIS is superior to the BPNN, and ANFIS can effectively and reliably construct an accurate flood forecast model. Copyright © 2005 John Wiley & Sons, Ltd.     

The data‐driven approach as an operational real‐time flood forecasting model

Accurate water level forecasts are essential for flood warning. This study adopts a data‐driven approach based on the adaptive network–based fuzzy inference system (ANFIS) to forecast the daily water levels of the Lower Mekong River at Pakse, Lao People's Democratic Republic. ANFIS is a hybrid system combining fuzzy inference system and artificial neural networks. Five ANFIS models were developed to provide water level forecasts from 1 to 5 days ahead, respectively. The results show that although ANFIS forecasts of water levels up to three lead days satisfied the benchmark, four‐ and five‐lead‐day forecasts were only slightly better in performance compared with the currently adopted operational model. This limitation is imposed by the auto‐ and cross‐correlations of the water level time series. Output updating procedures based on the autoregressive (AR) and recursive AR (RAR) models were used to enhance ANFIS model outputs. The RAR model performed better than the AR model. In addition, a partial recursive procedure that reduced the number of recursive steps when applying the AR or the RAR model for multi‐step‐ahead error prediction was superior to the fully recursive procedure. The RAR‐based partial recursive updating procedure significantly improved three‐, four‐ and five‐lead‐day forecasts. Our study further shows that for long lead times, ANFIS model errors are dominated by lag time errors. Although the ANFIS model with the RAR‐based partial recursive updating procedure provided the best results, this method was able to reduce the lag time errors significantly for the falling limbs only. Improvements for the rising limbs were modest. Copyright © 2011 John Wiley & Sons, Ltd.     

Seasonal Short‐Term Prediction of Dissolved Oxygen in Rivers via Nature‐Inspired Algorithms

This study challenges the use of three nature‐inspired algorithms as learning frameworks of the adaptive‐neuro‐fuzzy inference system (ANFIS) machine learning model for short‐term modeling of dissolved oxygen (DO) concentrations. Particle swarm optimization (PSO), butterfly optimization algorithm (BOA), and biogeography‐based optimization (BBO) are employed for developing predictive ANFIS models using seasonal 15 min data collected from the Rock Creek River in Washington, DC. Four independent variables are used as model inputs including water temperature (T), river discharge (Q), specific conductance (SC), and pH. The Mallow's Cp and R² parameters are used for choosing the best input parameters for the models. The models are assessed by several statistics such as the coefficient of determination (R²), root‐mean‐square error (RMSE), Nash–Sutcliffe efficiency, mean absolute error, and the percent bias. The results indicate that the performance of all‐nature‐inspired algorithms is close to each other. However, based on the calculated RMSE, they enhance the accuracy of standard ANFIS in the spring, summer, fall, and winter around 13.79%, 15.94%, 6.25%, and 12.74%, respectively. Overall, the ANFIS‐PSO and ANFIS‐BOA provide slightly better results than the other ANFIS models.     

Wavelet-ANFIS models for forecasting monsoon flows: Case study for the Gandak River (India)

WANFIS, a conjunction model of discreet wavelet transform (DWT) and adaptive neuro-fuzzy inference system (ANFIS) was developed for forecasting the current-day flow in a river when only available data are historical flows. Discreet wavelet transform decomposed the observed flow time series (OFTS) into wavelet components which captured useful information on three resolution levels. A smoothened flow time series (SFTS) was formed by filtering out the noise wavelet components and recombining the effective wavelet components. WANFIS model is essentially an ANFIS model with SFTS hydrograph as the input, while ANFIS and autoregression (AR) models, developed for comparison purpose, use OFTS hydrograph as input. For performance evaluation, the developed models were utilized for predicting daily monsoon flows for the Gandak River in Bihar state of India. During monsoon (June–October), this river carries large flows making the entire North Bihar unsafe for habitation or cultivation. Based on various performance indices, it was concluded that WANFIS models simulate the monsoon flows in the Gandak more reliably than ANFIS and AR models. The best performing WANFIS model, with four previous days’ flows as input, predicted the current-day Gandak flows with 80.7% accuracy while ANFIS and AR models predicted it with only 71.8 and 51.2% accuracies.     

Hydrological time‐series modelling using an adaptive neuro‐fuzzy inference system

Accurate forecasting of hydrological time‐series is a quite important issue for a wise and sustainable use of water resources. In this study, an adaptive neuro‐fuzzy inference system (ANFIS) approach is used to construct a time‐series forecasting system. In particular, the applicability of an ANFIS to the forecasting of the time‐series is investigated. To illustrate the applicability and capability of an ANFIS, the River Great Menderes, located in western Turkey, is chosen as a case study area. The advantage of this method is that it uses the input–output data sets. A total of 5844 daily data sets collected from 1985 to 2000 are used for the time‐series forecasting. Models having various input structures were constructed and the best structure was investigated. In addition, four various training/testing data sets were built by cross‐validation methods and the best data set was obtained. The performance of the ANFIS models in training and testing sets was compared with observations and also evaluated. In order to get an accurate and reliable comparison, the best‐fit model structure was also trained and tested by artificial neural networks and traditional time‐series analysis techniques and the results compared. The results indicate that the ANFIS can be applied successfully and provide high accuracy and reliability for time‐series modelling. Copyright © 2007 John Wiley & Sons, Ltd.     

Assessing uncertainty in refraction seismic traveltime inversion using a global inversion strategy

To analyse and invert refraction seismic travel time data, different approaches and techniques have been proposed. One common approach is to invert first‐break travel times employing local optimization approaches. However, these approaches result in a single velocity model, and it is difficult to assess the quality and to quantify uncertainties and non‐uniqueness of the found solution. To address these problems, we propose an inversion strategy relying on a global optimization approach known as particle swarm optimization. With this approach we generate an ensemble of acceptable velocity models, i.e., models explaining our data equally well. We test and evaluate our approach using synthetic seismic travel times and field data collected across a creeping hillslope in the Austrian Alps. Our synthetic study mimics a layered near‐surface environment, including a sharp velocity increase with depth and complex refractor topography. Analysing the generated ensemble of acceptable solutions using different statistical measures demonstrates that our inversion strategy is able to reconstruct the input velocity model, including reasonable, quantitative estimates of uncertainty. Our field data set is inverted, employing the same strategy, and we further compare our results with the velocity model obtained by a standard local optimization approach and the information from a nearby borehole. This comparison shows that both inversion strategies result in geologically reasonable models (in agreement with the borehole information). However, analysing the model variability of the ensemble generated using our global approach indicates that the result of the local optimization approach is part of this model ensemble. Our results show the benefit of employing a global inversion strategy to generate near‐surface velocity models from refraction seismic data sets, especially in cases where no detailed a priori information regarding subsurface structures and velocity variations is available.     

Soil creep and convex‐upward velocity profiles: theoretical and experimental investigation of disturbance‐driven sediment transport on hillslopes

The movement of unconsolidated materials near the Earth's surface is often driven by disturbances that occur at a range of spatial and temporal scales. The nature of these disturbances ranges from highly variable, such as tree turnover, to periodic and predictable, such as frost heave or creep. To explore the effect of probabilistic disturbances on surface processes, we formulated a granular creep model with analogy to rate process theory (RPT) used for chemical reactions. According to the theory, individual particles must be energized to a height greater than adjacent particles in order for grain dilation and transport to occur. The height of neighbouring particles (which is akin to activation energy in chemical reactions) varies with slope angle such that energy barriers get smaller in the downslope direction as slopes steepen. When slopes approach the friction‐limited angle of repose, the height of energy barriers approaches zero and grains ?ow in the absence of disturbance. An exponential function is used to describe the probability distribution of particle excitation height although alternative distributions are possible. We tested model predictions of granular dynamics in an experimental sandpile. In the sandpile, acoustic energy serves as the disturbance agent such that grains dilate and shear in response. Particle velocities are controlled by the frequency of energy pulses that result in grain displacement. Using tracer particles, we observed a convex‐upward velocity pro?le near the surface of the sandpile, consistent with predictions of our RPT‐based velocity model. In addition, we depth‐integrated the velocity model to predict how ?ux rates vary with inclination of the sandpile and observed non‐linear ?ux–gradient curves consistent with model predictions. By varying the acoustic energy level in the experimental sandpile, we documented changes in the rate of grain movement; similar changes in modelled velocities were achieved by varying the exponent of the particle excitation probability distribution. The general agreement between observed and modelled granular behaviour in our simple laboratory sandpile supports the utility of RPT‐based methods for modelling transport processes (e.g. soil creep, frost heave, and till deformation), thus enabling us to account for the probabilistic nature of disturbances that liberate sediment in natural landscapes. Copyright © 2004 John Wiley & Sons, Ltd.     

Non‐structure‐specific intensity measure parameters and characteristic period of near‐fault ground motions

This paper focuses on the effects of long‐period pulse of near‐fault ground motions on the structural damage potential. Two sets of near‐fault ground motion records from Chi‐Chi, Taiwan earthquake and Northridge earthquake with and without distinct pulse are selected as the input, and the correlation analysis between 30 non‐structure‐specific intensity measure parameters and maximum inelastic displacements and energy responses (input energy and hysteretic energy) of bilinear single degree of freedom systems are conducted. Based on the frequency characteristic of near‐fault ground motions with remarkable long‐period components, two intensity indices are proposed, namely, the improved effective peak acceleration (IEPA) and improved effective peak velocity (IEPV). In addition a new characteristic period of these ground motions is defined based on IEPA and IEPV. Numerical results illustrate that the intensity measure parameters related to ground acceleration present the best correlation with the seismic responses for rigid systems; the velocity‐related and displacement‐related parameters are better for medium‐frequency systems and flexible systems, respectively. The correlation curves of near‐fault ground motions with velocity pulse differ from those of ground motions without pulse. Moreover, the improved parameters IEPA and IEPV of near‐fault impulsive ground motions enhance the performance of intensity measure of corresponding conventional parameters, i.e. EPA and EPV. The new characteristic period based on IEPA and IEPV can better reflect the frequency content of near‐fault ground motions. Copyright © 2009 John Wiley & Sons, Ltd.     

Intelligent control for modelling of real‐time reservoir operation

This paper presents a new approach to improving real‐time reservoir operation. The approach combines two major procedures: the genetic algorithm (GA) and the adaptive network‐based fuzzy inference system (ANFIS). The GA is used to search the optimal reservoir operating histogram based on a given inflow series, which can be recognized as the base of input–output training patterns in the next step. The ANFIS is then built to create the fuzzy inference system, to construct the suitable structure and parameters, and to estimate the optimal water release according to the reservoir depth and inflow situation. The practicability and effectiveness of the approach proposed is tested on the operation of the Shihmen reservoir in Taiwan. The current M‐5 operating rule curves of the Shihmen reservoir are also evaluated. The simulation results demonstrate that this new approach, in comparison with the M‐5 rule curves, has superior performance with regard to the prediction of total water deficit and generalized shortage index (GSI). Copyright © 2001 John Wiley & Sons, Ltd.     

Adaptive neuro-fuzzy inference system for prediction of water level in reservoir

Accurate prediction of the water level in a reservoir is crucial to optimizing the management of water resources. A neuro-fuzzy hybrid approach was used to construct a water level forecasting system during flood periods. In particular, we used the adaptive network-based fuzzy inference system (ANFIS) to build a prediction model for reservoir management. To illustrate the applicability and capability of the ANFIS, the Shihmen reservoir, Taiwan, was used as a case study. A large number (132) of typhoon and heavy rainfall events with 8640 hourly data sets collected in past 31 years were used. To investigate whether this neuro-fuzzy model can be cleverer (accurate) if human knowledge, i.e. current reservoir operation outflow, is provided, we developed two ANFIS models: one with human decision as input, another without. The results demonstrate that the ANFIS can be applied successfully and provide high accuracy and reliability for reservoir water level forecasting in the next three hours. Furthermore, the model with human decision as input variable has consistently superior performance with regard to all used indexes than the model without this input.     

Dynamic force control with hydraulic actuators using added compliance and displacement compensation

A new approach to dynamic force control of mechanical systems, applicable in particular to frame structures, over frequency ranges spanning their resonant frequencies is presented. This approach is implemented using added compliance and displacement compensation. Hydraulic actuators are inherently velocity sources, that is, an electrical signal regulates their velocity response. Such systems are therefore by nature high‐impedance (mechanically stiff) systems. In contrast, for force control, a force source is required. Such a system logically would have to be a low‐impedance (mechanically compliant) system. This is achieved by intentionally introducing a flexible mechanism between the actuator and the structure to be excited. In addition, in order to obtain force control over frequencies spanning the structure's resonant frequency, a displacement compensation feedback loop is needed. The actuator itself operates in closed‐loop displacement control. The theoretical motivation, as well as the laboratory implementation of the above approach is discussed along with experimental results. Having achieved a means of dynamic force control, it can be applied to various experimental seismic simulation techniques such as the effective force method and the real‐time dynamic hybrid testing method. Copyright © 2008 John Wiley & Sons, Ltd.     

Developing a hybrid multi‐model for peak flood forecasting

The present study aims to develop a hybrid multi‐model using the soft computing approach. The model is a combination of a fuzzy logic, artificial neural network (ANN) and genetic algorithm (GA). While neural networks are low‐level computational structures that perform well dealing with raw data, fuzzy logic deal with reasoning on a higher level by using linguistic information acquired from domain experts. However, fuzzy systems lack the ability to learn and cannot adjust themselves to a new environment. Moreover, experts occasionally make mistakes and thus some rules used in a system may be false. A network type structure of the present hybrid model is a multi‐layer feed‐forward network, the main part is a fuzzy system based on the first‐order Sugeno fuzzy model with a fuzzification and a defuzzification processes. The consequent parameters are determined by least square method. The back‐propagation is applied to adjust weights of network. Then, the antecedent parameters of the membership function are updated accordingly by the gradient descent method. The GA was applied to select the fuzzy rule. The hybrid multi‐model was used to forecast the flood level at Chiang Mai (under the big flood 2005) and the Koriyama flood (2003) in Japan. The forecasting results are evaluated using standard global goodness of fit statistic, efficient index (EI), the root mean square error (RMSE) and the peak flood error. Moreover, the results are compared to the results of a neuro‐genetic model (NGO) and ANFIS model using the same input and output variables. It was found that the hybrid multi‐model can be used successfully with an efficiency index (EI) more than 0·95 (for Chiang Mai flood up to 12 h ahead forecasting) and more than 0·90 (for Koriyama flood up to 8 h ahead forecasting). In general, all of three models can predict the water level with satisfactory results. However, the hybrid model gave the best flood peak estimation among the three models. Therefore, the use of fuzzy rule base, which is selected by GA in the hybrid multi‐model helps to improve the accuracy of flood peak. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison of P‐wave attenuation models of wave‐induced flow

Wave‐induced oscillatory fluid flow in the vicinity of inclusions embedded in porous rocks is one of the main causes for P‐wave dispersion and attenuation at seismic frequencies. Hence, the P‐wave velocity depends on wave frequency, porosity, saturation, and other rock parameters. Several analytical models quantify this wave‐induced flow attenuation and result in characteristic velocity–saturation relations. Here, we compare some of these models by analyzing their low‐ and high‐frequency asymptotic behaviours and by applying them to measured velocity–saturation relations. Specifically, the Biot–Rayleigh model considering spherical inclusions embedded in an isotropic rock matrix is compared with White's and Johnson's models of patchy saturation. The modeling of laboratory data for tight sandstone and limestone indicates that, by selecting appropriate inclusion size, the Biot‐Rayleigh predictions are close to the measured values, particularly for intermediate and high water saturations.     

Computational fluid dynamics modelling of boundary roughness in gravel‐bed rivers: an investigation of the effects of random variability in bed elevation

Results from a series of numerical simulations of two‐dimensional open‐channel flow, conducted using the computational fluid dynamics (CFD) code FLUENT, are compared with data quantifying the mean and turbulent characteristics of open‐channel flow over two contrasting gravel beds. Boundary roughness effects are represented using both the conventional wall function approach and a random elevation model that simulates the effects of supra‐grid‐scale roughness elements (e.g. particle clusters and small bedforms). Results obtained using the random elevation model are characterized by a peak in turbulent kinetic energy located well above the bed (typically at y/h = 0·1–0·3). This is consistent with the field data and in contrast to the results obtained using the wall function approach for which maximum turbulent kinetic energy levels occur at the bed. Use of the random elevation model to represent supra‐grid‐scale roughness also allows a reduction in the height of the near‐bed mesh cell and therefore offers some potential to overcome problems experienced by the wall function approach in flows characterized by high relative roughness. Despite these benefits, the results of simulations conducted using the random elevation model are sensitive to the horizontal and vertical mesh resolution. Increasing the horizontal mesh resolution results in an increase in the near‐bed velocity gradient and turbulent kinetic energy, effectively roughening the bed. Varying the vertical resolution of the mesh has little effect on simulated mean velocity profiles, but results in substantial changes to the shape of the turbulent kinetic energy profile. These findings have significant implications for the application of CFD within natural gravel‐bed channels, particularly with regard to issues of topographic data collection, roughness parameterization and the derivation of mesh‐independent solutions. Copyright © 2001 John Wiley & Sons, Ltd.     

A stochastic model and synthesis for near‐fault impulsive ground motions

The orientations of ground motions are paramount when the pulse‐like motions and their unfavorable seismic responses are considered. This paper addresses the stochastic modeling and synthesizing of near‐fault impulsive ground motions with forward directivity effect taking the orientation of the strongest pulses into account. First, a statistical parametric analysis of velocity time histories in the orientation of the strongest pulse with a specified magnitude and various fault distances is performed. A new stochastic model is established consisting of a velocity pulse model with random parameters and a stochastic approach to synthesize high‐frequency velocity time history. The high‐frequency velocity history is achieved by integrating a stochastic high‐frequency accelerogram, which is generated via the modified K‐T spectrum of residual acceleration histories and then modulated by the specific envelope function. Next, the associated parameters of pulse model, envelope function, and power spectral density are estimated by the least‐square fitting. Some chosen parameters in the stochastic model of near‐fault motions based on correlation analysis are regarded as random variables, which are validated to follow the normal or lognormal distribution. Moreover, the number theoretical method is suggested to select efficiently representative points, for generating artificial near‐fault impulsive ground motions with the feature of the strongest pulse, which can be used to the seismic response and reliability analysis of critical structures conveniently. Finally, the simulated ground motions demonstrate that the synthetic ground motions generated by the proposed stochastic model can represent the impulsive characteristic of near‐fault ground motions. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive neural-based fuzzy inference system (ANFIS) approach for modelling hydrological time series

Abstract

The main aim of this study is to develop a flow prediction method, based on the adaptive neural-based fuzzy inference system (ANFIS) coupled with stochastic hydrological models. An ANFIS methodology is applied to river flow prediction in Dim Stream in the southern part of Turkey. Application is given for hydrological time series modelling. Synthetic series, generated through autoregressinve moving-average (ARMA) models, are then used for training data sets of the ANFIS. It is seen that the extension of input and output data sets in the training stage improves the accuracy of forecasting by using ANFIS.     

Modelling long‐term contaminant migration in a catchment at fine spatial and temporal scales using the UP system

A method has been developed to simulate the long‐term migration of radionuclides in the near‐surface of a river catchment, following their release from a deep underground repository for radioactive waste. Previous (30‐year) simulations, conducted using the SHETRAN physically based modelling system, showed that long‐term (many decades) simulations are required to allow the system to reach steady state. Physically based, distributed models, such as SHETRAN, tend to be too computationally expensive for this task. Traditional lumped catchment‐scale models, on the other hand, do not give sufficiently detailed spatially distributed results. An intermediate approach to modelling has therefore been developed which allows flow and transport processes to be simulated with the spatial resolution normally associated with distributed models, whilst being computationally efficient.The approach involves constructing a lumped model in which the catchment is represented by a number of conceptual water storage compartments. The flow rates to and from these compartments are prescribed by functions that summarize the results from physically based distributed models run for a range of characteristic flow regimes. The physically based models used were, SHETRAN for the subsurface compartments, a particle tracking model for overland flow and an analytical model for channel routing. One important advantage of the method used in constructing the lumped model is that it makes down scaling possible, in the sense that fine‐scale information on the distributed hydrological regime, as simulated by the physically based distributed models, can be inferred from the variables in the lumped model that describe the hydrology at the catchment scale. A 250‐year flow simulation has been run and the down scaling process used to infer a 250‐year time‐series of three‐dimensional velocity fields for the subsurface of the catchment. This series was then used to drive a particle tracking simulation of contaminant migration. The concentration and spatial distribution of contaminants simulated by this model for the first 30 years were in close agreement with SHETRAN results. The remaining 220 years highlighted the fact that some of the most important transport pathways to the surface carry contaminants only very slowly so both the magnitude and spatial distribution of concentration in surface soils are not apparent over the shorter SHETRAN simulations. Copyright © 1999 John Wiley & Sons, Ltd.     

A model for distributed GIUH‐based flow routing on natural and anthropogenic hillslopes

Attempts to reduce the number of parameters in distributed rainfall–runoff models have not yet resulted in a model that is accurate for both natural and anthropogenic hillslopes. We take on the challenge by proposing a distributed model for overland flow and channel flow based on a combination of a linear response time distribution and the hillslope geomorphologic instantaneous unit hydrograph (GIUH), which can be calculated with only a digital elevation model and a map with field boundaries and channel network as input. The spatial domain is subdivided into representative elementary hillslopes (REHs) for each of which we define geometric and flow velocity parameters and compute the GIUH. The catchment GIUH is given by the sum of all REH responses. While most distributed models only perform well on natural hillslopes, the advantage of our approach is that it can also be applied to modified hillslopes with for example a rectangular drainage network and terrace cultivation. Tests show that the REH‐GIUH approach performs better than classical routing functions (exponential and gamma). Simulations of four virtual hillslopes suggest that peak flow at the catchment outlet is directly related to drainage density. By combining the distributed flow routing model with a lumped‐parameter infiltration model, we were also able to demonstrate that terrace cultivation delays the response time and reduces peak flow in comparison to the same hillslope, but with a natural stream network. The REH‐GIUH approach is a first step in the process of coupling distributed hydrological models to erosion and water quality models at the REH (associated with agricultural management) and at the catchment scale (associated with the evaluation of the environmental impact of human activities). It furthermore provides a basis for the development of models for large catchments and urban or peri‐urban catchments. Copyright © 2013 John Wiley & Sons, Ltd.     

Fuzzy computing based rainfall–runoff model for real time flood forecasting

This paper analyses the skills of fuzzy computing based rainfall–runoff model in real time flood forecasting. The potential of fuzzy computing has been demonstrated by developing a model for forecasting the river flow of Narmada basin in India. This work has demonstrated that fuzzy models can take advantage of their capability to simulate the unknown relationships between a set of relevant hydrological data such as rainfall and river flow. Many combinations of input variables were presented to the model with varying structures as a sensitivity study to verify the conclusions about the coherence between precipitation, upstream runoff and total watershed runoff. The most appropriate set of input variables was determined, and the study suggests that the river flow of Narmada behaves more like an autoregressive process. As the precipitation is weighted only a little by the model, the last time‐steps of measured runoff are dominating the forecast. Thus a forecast based on expected rainfall becomes very inaccurate. Although good results for one‐step‐ahead forecasts are received, the accuracy deteriorates as the lead time increases. Using the one‐step‐ahead forecast model recursively to predict flows at higher lead time, however, produces better results as opposed to different independent fuzzy models to forecast flows at various lead times. Copyright © 2004 John Wiley & Sons, Ltd.     

Dominant pulse simulation of near fault ground motions

In this study, a new mathematical model is developed composed of two parts, including harmonic and polynomial expressions for simulating the dominant velocity pulse of near fault ground motions. Based on a proposed velocity function, the corresponding expressions for the ground acceleration and displacement time histories are also derived. The proposed model is then fitted using some selected pulse-like near fault ground motions in the Next Generation Attenuation (NGA) project library. The new model is not only simple in form but also simulates the long-period portion of actual velocity near fault records with a high level of precision. It is shown that the proposed model-based elastic response spectra are compatible with the near fault records in the neighborhood of the prevailing frequency of the pulse. The results indicate that the proposed model adequately simulates the components of the time histories. Finally, the energy of the proposed pulse was compared with the energy of the actual record to confirm the compatibility.