Gurhan Gurarslan

Parameter Estimation of the Nonlinear Muskingum Flood-Routing Model Using a Hybrid Harmony Search Algorithm

AbstractIn this paper, a hybrid harmony search (HS) algorithm is proposed for the parameter estimation of the nonlinear Muskingum model. The BFGS algorithm is used as local search algorithm with a low probability for accelerating the HS algorithm. In the proposed technique, an indirect penalty function approach is imposed on the model to prevent negativity of outflows and storages. The proposed algorithm finds the global or near-global minimum regardless of the initial parameter values with fast convergence. The proposed algorithm found the best solution among 12 different methods. The results demonstrate that the proposed algorithm can be applied confidently to estimate optimal parameter values of the nonlinear Muskingum model. Moreover, this hybrid methodology may be applicable to any continuous engineering optimization problems.

Hybridizing the harmony search algorithm with a spreadsheet ‘Solver’ for solving continuous engineering optimization problems

In this article, a hybrid global–local optimization algorithm is proposed to solve continuous engineering optimization problems. In the proposed algorithm, the harmony search (HS) algorithm is used as a global-search method and hybridized with a spreadsheet ‘Solver’ to improve the results of the HS algorithm. With this purpose, the hybrid HS–Solver algorithm has been proposed. In order to test the performance of the proposed hybrid HS–Solver algorithm, several unconstrained, constrained, and structural-engineering optimization problems have been solved and their results are compared with other deterministic and stochastic solution methods. Also, an empirical study has been carried out to test the performance of the proposed hybrid HS–Solver algorithm for different sets of HS solution parameters. Identified results showed that the hybrid HS–Solver algorithm requires fewer iterations and gives more effective results than other deterministic and stochastic solution algorithms.

A sixth-order compact finite difference scheme to the numerical solutions of Burgers' equation

Abstract A numerical solution of the one-dimensional Burgers’ equation is obtained using a sixth-order compact finite difference method. To achieve this, a tridiagonal sixth-order compact finite difference scheme in space and a low-storage third-order total variation diminishing Runge–Kutta scheme in time have been combined. The scheme is implemented to solve two test problems with known exact solutions. Comparisons of the computed results with exact solutions showed that the method is capable of achieving high accuracy and efficiency with minimal computational effort. The present results are also seen to be more accurate than some available results given in the literature.

A new nonlinear Muskingum flood routing model incorporating lateral flow

A new nonlinear Muskingum flood routing model taking the contribution from lateral flow into consideration was developed in the present study. The cuckoo search algorithm, a quite novel and robust algorithm, was used in the calibration and verification of the model parameters. The success and the dependability of the proposed model were tested on five different sets of synthetic and real flood data. The optimal solutions for the test cases were determined by the currently proposed model rather than by different models taken from the literature, indicating that this model could be suitable for use in flood routing problems.

Numerical Solution of Advection-Diffusion Equation Using a Sixth-Order Compact Finite Difference Method

This study aims to produce numerical solutions of one-dimensional advection-diffusion equation using a sixth-order compact difference scheme in space and a fourth-order Runge-Kutta scheme in time. The suggested scheme here has been seen to be very accurate and a relatively flexible solution approach in solving the contaminant transport equation for . For the solution of the present equation, the combined technique has been used instead of conventional solution techniques. The accuracy and validity of the numerical model are verified through the presented results and the literature. The computed results showed that the use of the current method in the simulation is very applicable for the solution of the advection-diffusion equation. The present technique is seen to be a very reliable alternative to existing techniques for these kinds of applications.

Numerical Solutions of the Generalized Burgers-Huxley Equation by a Differential Quadrature Method

Numerical solutions of the generalized Burgers-Huxley equation are obtained using a polynomial differential quadrature method with minimal computational effort. To achieve this, a combination of a polynomial-based differential quadrature method in space and a low-storage third-order total variation diminishing Runge-Kutta scheme in time has been used. The computed results with the use of this technique have been compared with the exact solution to show the required accuracy of it. Since the scheme is explicit, linearization is not needed and the approximate solution to the nonlinear equation is obtained easily. The effectiveness of this method is verified through illustrative examples. The present method is seen to be a very reliable alternative method to some existing techniques for such realistic problems.

Solving inverse problems of groundwater-pollution-source identification using a differential evolution algorithm

In this study, an accurate model was developed for solving problems of groundwater-pollution-source identification. In the developed model, the numerical simulations of flow and pollutant transport in groundwater were carried out using MODFLOW and MT3DMS software. The optimization processes were carried out using a differential evolution algorithm. The performance of the developed model was tested on two hypothetical aquifer models using real and noisy observation data. In the first model, the release histories of the pollution sources were determined assuming that the numbers, locations and active stress periods of the sources are known. In the second model, the release histories of the pollution sources were determined assuming that there is no information on the sources. The results obtained by the developed model were found to be better than those reported in literature.RésuméDans cette étude, un modèle précis a été développé pour résoudre les problèmes d’identification de la source de pollution des eaux souterraines. Dans le modèle développé, les simulations numériques d’écoulement et de transport de polluant dans les eaux souterraines ont été réalisées en utilisant les logiciels MODFLOW et MT3DMS et les processus d’optimisation ont été conduits au moyen d’un algorithme d’évolution différentielle. La performance du modèle développé a été testée sur deux modèles d’aquifères hypothétiques en utilisant des données d’observation réelles et bruitées. Dans le premier modèle, les historiques d’émission par les sources de pollution ont été déterminés en faisant l’hypothèse selon laquelle les nombres, les localisations et les périodes d’activité des sources sont connus. Dans le second modèle, les historiques d’émission par les sources de pollution ont été déterminés en faisant l’hypothèse qu’il n’y a pas d’information sur les sources. Les résultats obtenus au moyen du modèle développé sont meilleurs que ceux rapportés dans la littérature.ResumenEn este estudio, se desarrolló un modelo exacto para la resolución de problemas de identificación de fuentes de contaminación de agua subterránea. En el modelo desarrollado, las simulaciones numéricas de flujo y de transporte de contaminantes en el agua subterránea se llevaron a cabo usando los softwares MODFLOW y MT3DMS, y el proceso de optimización fue realizado utilizando un algoritmo diferencial de evolución. El rendimiento del modelo desarrollado se probó con dos modelos de acuíferos hipotéticos usando datos observacionales reales y ruidosos. En el primer modelo, las historias de los vertidos de las fuentes de contaminación se determinaron suponiendo conocidos los números, ubicaciones y períodos activos de las fuentes. En el segundo modelo, las historias de los vertidos de las fuentes de contaminación se determinaron suponiendo que no hay ninguna información sobre las fuentes. Se encontró que los resultados obtenidos por el modelo desarrollado eran mejores que los informados en la literatura.摘要在这项研究中,建立了准确模型来解决地下水污染源识别问题。在开发的模型中,采用MODFLOW和MT3DMS软件进行了地下水水流和污染物运移的数值模拟,并且采用差分进化算法进行了最优化处理。利用真实和众多的观测数据在两个假设含水层模型上对开发模型的性能进行了测试。第一个模型中,假定污染源的数量、位置和有效压力期已知,确定了污染源的释放历史。第二个模型中,假定没有污染源的任何信息,确定了污染源的释放历史。发现,所开发的模型获取的结果比文献记载的要好。ResumoNesse estudo, um modelo acurado foi desenvolvido para solucionar problemas de identificação de fontes de poluição das águas subterrâneas. No modelo desenvolvido, as simulações numéricas de fluxo e transporte de poluentes foram conduzidas usando os softwares MODFLOW e MT3DMS, e o processo de otimização foi conduzido usando um algoritmo de evolução diferencial. O desempenho do modelo desenvolvido foi testado em dois modelos de aquíferos hipotéticos usando dados de observações reais e com ruído. No primeiro modelo, os históricos de liberação de fontes de poluição foram determinados assumindo que os números, locais e períodos de estresse ativo das fontes são conhecidos. No segundo modelo, os históricos de liberação de fontes de poluição foram determinados assumindo que não existe informação sobre as fontes. Os resultados obtidos pelo modelo desenvolvido foram considerados melhores do que aqueles referenciados na literatura.ÖzetBu çalışmada, yeraltısuyu-kirlilik-kaynağı belirlenmesi ters problemlerinin çözümü için doğruluğu yüksek bir model geliştirilmiştir. Geliştirilen modelde, yeraltısuyunda akım ve kirletici taşınımı denklemlerinin sayısal simülasyonları MODFLOW ve MT3DMS yazılımları, optimizasyon işlemleri ise diferansiyel gelişim algoritması kullanılarak gerçekleştirilmiştir. Geliştirilen modelin performansı, iki adet kurgusal akifer modeli üzerinde gerçek ve hatalı gözlem verileri kullanılarak test edilmiştir. Birinci modelde, kaynakların yerleri ve sayılarının bilindiği varsayılarak kirletici kaynakların boşalım geçmişleri elde edilmiştir. İkinci modelde ise kaynaklarla ilgili herhangi bir bilgi olmadığı varsayılarak kirletici kaynakların boşalım geçmişleri belirlenmiştir. Geliştirilen modelden elde edilen sonuçların, literatürde verilen sonuçlardan daha iyi olduğu görülmüştür.

Discussion of “Estimation of Nonlinear Muskingum Model Parameter Using Differential Evolution” by Dong-Mei Xu, Lin Qiu, and Shou-Yu Chen

The discussers appreciate the authors and their valuable study, but consider it necessary to clarify the several issues to prevent misunderstandings and wrong evaluations regarding the application of the differential evolution (DE) method to the nonlinear Muskingum model. The authors state that they applied the procedure given in Geem (2006) as a routing algorithm. However, although the χ, m, and SSQ values that the authors obtained conform to the results of the study given in literature, the K parameter is considerably different. The routing procedure proposed in Tung (1985) and Geem (2006), also used by the authors, were coded in a Matlab environment by the discussers. When the parameters that the authors give as an optimum solution (K 1⁄4 0.5175, χ 1⁄4 0.2869, m 1⁄4 1.8680) were placed in this code, the values given in Table 1 were obtained. It is necessary to state that unit time was used in the routing procedure proposed in Tung (1985) and Geem (2006), and this situation was explained in the related references (Geem 2011; Karahan et al. 2013). The authors stated that they used the routing procedure proposed in Geem (2006) in their studies. In this case, as shown in the fourth column of Table 1, outflow values calculated forΔt 1⁄4 1 h are so different than the measured values that the measured SSQ value becomes 19956.4461. Outflow values given by the authors are only obtained for Δt 1⁄4 6 h; this value was calculated by the discussers and presented in the last column of Table 1. If the authors, as they state, have exactly followed routing procedure proposed in Geem (2006), like other parameters for the same objective function, the K parameter should conform to the values given in literature. This situation has to be clarified. Generally, the selection of the solution space of the parameters in optimization problems plays an important role with respect to solution quality. If the approximate solutions of these parameters are known a priori, then an optimal parameter value can easily be determined by using any heuristic or gradient-based method (Karahan 2013). Input and output hydrograph values are used to determine nonlinear Muskingum model parameters. Wilson data (Wilson 1974), which was used for test purposes in this study, was also used by many researchers in the literature and is a problem whose solution space was known formerly. The parameter space used for Wilson data in literature is generally K 1⁄4 0–0.20, χ 1⁄4 0.2–0.3 and m 1⁄4 1.5–2.5 (Kim et al. 2001). The authors did not explain which range they selected as parameter space in the paper. This is a significant absence in terms of testing analysis. Since there is no information about this subject in the paper, random solution vectors of the same number as the population number (NP 1⁄4 30) that the authors used were produced by using the solution space given above and presented in Table 2. Let r1, r2, and r3 values be randomly chosen as 5, 9, and 21, respectively. In this case, the obtained trial vector is (0.0993039, 0.314946, 1.374150) in the mutation step. The output hydrograph corresponding to this vector is given in Table 3. As seen in Table 3, output hydrograph values in between 84–126 hours are complex numbers and meaningless in a physical sense. SSQ value for the stated output hydrograph is −3.73Eþ 05-ð2.58Eþ 05Þi. The calculated SSQ value is also a complex number, which results in preventing the application of the selection operator of the DE algorithm and the collapse of the optimization algorithm. Routing procedure that will be applied for the application of the DE in determination of nonlinear Muskingum parameters must be different than the one given in the paper—or, to apply the given procedure, it is necessary to know the solution previously and to search it in a narrow range around the optimum solution. Undoubtedly, if the solution is known formerly, an optimization process is not required. Therefore, the authors must clearly state the routing procedure they followed and the parameter space they used. The discussers downloaded differential evolution (DE) code (Price and Storn 2012) and determined nonlinear Muskingum model parameters for three different solution spaces given in Table 4 by using the routing procedure given in Geem (2006). All calculations were repeated 1,000 times in order to reduce to a minimum level the dependence of the used algorithm on the initial values, and analyses results were summarized in Table 5 and Table 6. The global solution, near-global solution, and unfeasible solution expressed in Table 5 and Table 6 show the values of SSQ 1⁄4 36.7679, SSQ 1⁄4 36.7680, and SSQ > 36.7680, respectively. Table 1. Computed Outflow Values

Accurate Simulation of Contaminant Transport Using High-Order Compact Finite Difference Schemes

Numerical simulation of advective-dispersive contaminant transport is carried out by using high-order compact finite difference schemes combined with second-order MacCormack and fourth-order Runge-Kutta schemes. Both of the two schemes have accuracy of sixth-order in space. A sixth-order MacCormack scheme is proposed for the first time within this study. For the aim of demonstrating efficiency and high-order accuracy of the current methods, some numerical experiments have been done. The schemes are implemented to solve two test problems with known exact solutions. It has been exhibited that the methods are capable of succeeding high accuracy and efficiency with minimal computational effort, by comparisons of the computed results with exact solutions.

Approximate solutions of linear and non-linear diffusion equations by using Daftardar-Gejji-Jafari’s method

This study discovers the utility of the Daftardar-Gejji-Jafari’s (DGJ) method to obtain approximate solution of the linear and non-linear diffusion equations. The method gives reliable results in the form of analytical approximation. Thus, the method is seen to be a very reliable alternative tool for finding analytical solutions of more complex equations. Use of small parameter or linearisation is not needed in the present approach as opposed to numerical methods. The aim of this work is to derive approximations to the solution of the diffusion equations. The method and its ability are illustrated in solving seven examples. The obtained solutions converge to the analytical solutions and are in very good agreement with the literature. The proposed method is realised to be more cost-effective in terms of computation. The DGJ method is seen to be a very good alternative to existing iterative techniques.