Consultant Mathematical Modeller

Swindon, United Kingdom

Consultant Mathematical Modeller

Swindon, United Kingdom
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Ghorbani M.A.,University of Tabriz | Khatibi R.,Consultant Mathematical Modeller | Sivakumar B.,University of New South Wales | Sivakumar B.,University of California at Davis | Cobb L.,University of Colorado at Denver
Hydrological Sciences Journal | Year: 2010

Modelling and prediction of hydrological processes (e.g. rainfall-runoff) can be influenced by discontinuities in observed data, and one particular case may arise when the time scale (i.e. resolution) is coarse (e.g. monthly). This study investigates the application of catastrophe theory to examine its suitability to identify possible discontinuities in the rainfall-runoff process. A stochastic cusp catastrophe model is used to study possible discontinuities in the monthly rainfall-runoff process at the Aji River basin in Azerbaijan, Iran. Monthly-averaged rainfall and flow data observed over a period of 20 years (1981-2000) are analysed using the Cuspfit program. In this model, rainfall serves as a control variable and runoff as a behavioural variable. The performance of this model is evaluated using four measures: correlation coefficient, log-likelihood, Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results indicate the presence of discontinuities in the rainfall-runoff process, with a significant sudden jump in flow (cusp signal) when rainfall reaches a threshold value. The performance of the model is also found to be better than that of linear and logistic models. The present results, though preliminary, are promising in the sense that catastrophe theory can play a possible role in the study of hydrological systems and processes, especially when the data are noisy. © 2010 IAHS Press.


Khatibi R.,Consultant Mathematical Modeller | Sivakumar B.,University of New South Wales | Sivakumar B.,University of California at Davis | Ghorbani M.A.,University of Tabriz | And 3 more authors.
Journal of Hydrology | Year: 2012

The existence of chaotic behaviour in the river stage and discharge time series observed at the Sogutluhan hydrometric station, Turkey, is investigated. Five nonlinear dynamic methods are employed: (1) phase space reconstruction; (2) False Nearest Neighbour (FNN) algorithm; (3) correlation dimension method; (4) Lyapunov exponent method; and (5) local approximation method. These methods have their bases on data embedding, nearest neighbour search, dimensionality analysis, system divergence/convergence, and local approximation and have varying levels of sophistication in conceptualisation and implementation. They provide either direct identification of chaotic behaviour or at least facilitate identification through system reconstruction, complexity determination (especially in terms of dimensionality), and prediction (including predictability horizon). As the discharge data used in this study are produced by rating directly gauged stage time series, it becomes feasible to investigate any interference triggered by chaotic signals with the rating. The results indicate the existence of low-dimensional chaos in the two time series. They also suggest that the rating of the stage time series to obtain the discharge time series amplifies significantly the fluctuations in the latter in the presence of chaotic signals. © 2011 Elsevier B.V.


Khatibi R.,Consultant Mathematical Modeller | Ghorbani M.A.,University of Tabriz | Kashani M.H.,University of Tabriz | Kisi O.,Erciyes University
Journal of Hydrology | Year: 2011

The inter-comparison of three artificial intelligence (AI) techniques are presented using the results of river flow/stage timeseries, that are otherwise handled by traditional discharge routing techniques. These models comprise Artificial Neural Network (ANN), Adaptive Nero-Fuzzy Inference System (ANFIS) and Genetic Programming (GP), which are for discharge routing of Kizilirmak River, Turkey. The daily mean river discharge data with a period between 1999 and 2003 were used for training and testing the models. The comparison includes both visual and parametric approaches using such statistic as Coefficient of Correlation (CC), Mean Absolute Error (MAE) and Mean Square Relative Error (MSRE), as well as a basic scoring system. Overall, the results indicate that ANN and ANFIS have mixed fortunes in discharge routing, and both have different abilities in capturing and reproducing some of the observed information. However, the performance of GP displays a better edge over the other two modelling approaches in most of the respects. Attention is given to the information contents of recorded timeseries in terms of their peak values and timings, where one performance measure may capture some of the information contents but be ineffective in others. Thus, this makes a case for compiling knowledge base for various modelling techniques. © 2011 Elsevier B.V.


Khatibi R.,Consultant Mathematical Modeller | Naghipour L.,University of Tabriz | Ghorbani M.A.,University of Tabriz | Smith M.S.,6715 n. table mt. rd. | And 4 more authors.
Atmospheric Environment | Year: 2013

Predictive ozone models are becoming indispensable tools by providing a capability for pollution alerts to serve people who are vulnerable to the risks. We have developed a tropospheric ozone prediction capability for Tabriz, Iran, by using the following five modeling strategies: three regression-type methods: Multiple Linear Regression (MLR), Artificial Neural Networks (ANNs), and Gene Expression Programming (GEP); and two auto-regression-type models: Nonlinear Local Prediction (NLP) to implement chaos theory and Auto-Regressive Integrated Moving Average (ARIMA) models. The regression-type modeling strategies explain the data in terms of: temperature, solar radiation, dew point temperature, and wind speed, by regressing present ozone values to their past values. The ozone time series are available at various time intervals, including hourly intervals, from August 2010 to March 2011. The results for MLR, ANN and GEP models are not overly good but those produced by NLP and ARIMA are promising for the establishing a forecasting capability. © 2012 Elsevier Ltd.


Khatibi R.,Consultant Mathematical Modeller | Ghorbani M.A.,University of Tabriz | Naghipour L.,University of Tabriz | Jothiprakash V.,Indian Institute of Technology Bombay | And 2 more authors.
Journal of Hydrology | Year: 2014

Five modeling strategies are employed to analyze water level time series of six lakes with different physical characteristics such as shape, size, altitude and range of variations. The models comprise chaos theory, Auto-Regressive Integrated Moving Average (ARIMA) - treated for seasonality and hence SARIMA, Artificial Neural Networks (ANN), Gene Expression Programming (GEP) and Multiple Linear Regression (MLR). Each is formulated on a different premise with different underlying assumptions. Chaos theory is elaborated in a greater detail as it is customary to identify the existence of chaotic signals by a number of techniques (e.g. average mutual information and false nearest neighbors) and future values are predicted using the Nonlinear Local Prediction (NLP) technique. This paper takes a critical view of past inter-comparison studies seeking a superior performance, against which it is reported that (i) the performances of all five modeling strategies vary from good to poor, hampering the recommendation of a clear-cut predictive model; (ii) the performances of the datasets of two cases are consistently better with all five modeling strategies; (iii) in other cases, their performances are poor but the results can still be fit-for-purpose; (iv) the simultaneous good performances of NLP and SARIMA pull their underlying assumptions to different ends, which cannot be reconciled. A number of arguments are presented including the culture of pluralism, according to which the various modeling strategies facilitate an insight into the data from different vantages. © 2014 Elsevier B.V.


Khatibi R.,Consultant Mathematical Modeller | Salmasi F.,University of Tabriz | Ghorbani M.A.,University of Tabriz | Asadi H.,University of Tabriz
Water Resources Management | Year: 2014

The hydraulics of energy dissipation over stepped-gabion weirs is investigated by carrying out a series of laboratory experiments, building models to explain the experimental data, and testing their robustness by using the data reported by other researchers. The experiments comprise: six different stepped-gabion weirs tested in a horizontal laboratory flume, a wide range of discharge values, two weir slopes (V:H): 1:1 and 1:2, and gabion filling material gravel size (porosity equal to 38 %, 40 % and 42 %). These experimental setups were selected to ensure the development of both the nappe and skimming flow regimes within the measured dataset. The models developed for computing energy dissipation over stepped-gabion weirs comprise: multiple regression equations based on dimensional analysis theory, Artificial Neural Network (ANN) and Gene Expression Programming (GEP). The analysis shows that the measured data capture both flow regimes and the transition in between them and above all, and by using all of the data, it may be possible to identify the range of each regime. Energy dissipation modelled by the ANN formulation is successful and may be recommended for reliable estimates but those by GEP and regression analysis can still serve for rough-and-ready estimates in engineering applications. © 2014 Springer Science+Business Media Dordrecht.


Khatibi R.,Consultant Mathematical Modeller | Naghipour L.,University of Tabriz | Ghorbani M.A.,University of Tabriz | Aalami M.T.,University of Tabriz
Neural Computing and Applications | Year: 2013

Recorded time series of relative humidity (RH) are modeled by using genetic expression programming (GEP) and artificial neural networks (ANNs) models. The data are noisy and contain missing datapoints. RH is modeled as a function of three meteorological variables: temperature, wind speed, and pressure. Various model structures of both of these models are investigated with the aim of testing the robustness of the predicted values in the presence of noise and missing data. Due to the presence of noise, a sophisticated treatment of missing data was not justifiable, and therefore, the strategy adopted was just to carry the datapoints backward, although this may induce bias in the time dimension and contaminate the predicted results. The results of this study indicate that through a careful selection of model structures both GEP and ANN can produce adequately reliable prediction of RH values 1 year into the future. The paper provides evidence that this model structure is feasible when the dependent variables include both the present and past values. © 2012 Springer-Verlag London Limited.


Khatibi R.,Consultant Mathematical Modeller | Ghorbani M.A.,University of Tabriz | Aalami M.T.,University of Tabriz | Kocak K.,Technical University of Istanbul | And 3 more authors.
Ocean Dynamics | Year: 2011

Water level forecasting using recorded time series can provide a local modelling capability to facilitate local proactive management practices. To this end, hourly sea water level time series are investigated. The records collected at the Hillarys Boat Harbour, Western Australia, are investigated over the period of 2000 and 2002. Two modelling techniques are employed: low-dimensional dynamic model, known as the deterministic chaos theory, and genetic programming, GP. The phase space, which describes the evolution of the behaviour of a nonlinear system in time, was reconstructed using the delay-embedding theorem suggested by Takens. The presence of chaotic signals in the data was identified by the phase space reconstruction and correlation dimension methods, and also the predictability into the future was calculated by the largest Lyapunov exponent to be 437 h or 18 days into the future. The intercomparison of results of the local prediction and GP models shows that for this site-specific dataset, the local prediction model has a slight edge over GP. However, rather than recommending one technique over another, the paper promotes a pluralistic modelling culture, whereby different techniques should be tested to gain a specific insight from each of the models. This would enable a consensus to be drawn from a set of results rather than ignoring the individual insights provided by each model. © 2011 Springer-Verlag.

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