Shuffled Complex Evolution Method Research Articles

Development of Equations for Meander Movement Velocities by SCE Optimization Algorithm based on Experimental Study

Meandering rivers have a dynamic planform, which means that rivers move in radial direction with variable velocities. The movement velocities can be estimated from historical maps of specific river or using mathematical approach. There is not explicit method or suitable algebraic equation for estimation of river meander movement velocities. In this study, experiments were carried out in a laboratory flume, to develop novel equations to calculate meandering river movement velocities. We designated these empirical equations as the river resistance equations. The experiments were conducted with non-uniform, nonchosive sediment in a re-circulating flume with changeable slopes. The influence of bankfull discharge, bed slope and channel width on the meander movement velocities were discussed. Based on the experimental data, three novel empirical equations for prediction of Wx and Wexp and Wm were proposed. Moreover, the shuffled complex evolution (SCE) optimization algorithm was used to estimate the unknown parameters of the empirical equations. To validate SCE method, the result was compared with traditional multiple regression analysis. This comparison indicated that the SCE optimization algorithm outperformed the multiple regression analysis method in the empirical equations calibration.

Thermal degradation of bituminous coal with both model-free and model-fitting methods

A series of thermogravimetric experiments was conducted to study the thermal degradation of bituminous coal at various heating rates in both nitrogen and air atmosphere. Both model-free and model-fitting methods were applied simultaneously to explore the reaction kinetic parameters. The activation energies were estimated in the range of 194.7–348.0 kJ/mol at different conversions by two typical model-free methods (Flynn-Wall-Ozawa and Kissinger-Akahira-Sunose methods). Shuffled Complex Evolution method (SCE), as the representative of model-fitting method, was firstly used in the coal pyrolysis process. By comparison, the predicted activation energy (199.2 kJ/mol) by model-fitting method was just within the range of values obtained by the model-free methods, validating the applicability of this model-fitting method. Furthermore, the effect of char oxidation and its kinetic parameters are analyzed by SCE based on the difference of nitrogen and air atmosphere. These optimized parameters can be coupled with the pyrolysis model and applied in the following energy conversion processes.

Hydrologic Impacts of Ensemble-RCM-Projected Climate Changes in the Athabasca River Basin, Canada

Abstract In this study, the Providing Regional Climates for Impacts Studies (PRECIS) and the Regional Climate Model (RegCM) system as well as the Variable Infiltration Capacity (VIC) macroscale hydrologic model were integrated into a general framework to investigate impacts of future climates on the hydrologic regime of the Athabasca River basin. Regional climate models (RCMs) including PRECIS and RegCM were used to develop ensemble high-resolution climate projections for 1979–2099. RCMs were driven by the boundary conditions from the Hadley Centre Global Environment Model, version 2 with Earth system configurations (HadGEM2-ES); the Second Generation Canadian Earth System Model (CanESM2); and the Geophysical Fluid Dynamics Laboratory Earth System Model with MOM (GFDL-ESM2M) under the representative concentration pathways (RCPs). The ensemble climate simulations were validated through comparison with observations for 1984–2003. The RCMs project increases in temperature, precipitation, and wind speed under RCPs across most of the Athabasca River basin. Meanwhile, VIC was calibrated using the University of Arizona Shuffled Complex Evolution method (SCE-UA). The performance of the VIC model in replicating the characteristics of the observed streamflow was validated for 1994–2003. Changes in runoff and streamflow under RCPs were then simulated by the validated VIC model. The validation results demonstrate that the ensemble-RCM-driven VIC model can effectively reproduce historical climatological and hydrological patterns in the Athabasca River basin. The ensemble-RCM-driven VIC model shows that monthly streamflow is projected to increase in the 2050s and 2080s under RCPs, with notably higher flows expected in the spring for the 2080s. This will have substantial impacts on water balance on the Athabasca River basin, thus affecting the surrounding industry and ecosystems. The developed framework can be applied to other regions for exploration of hydrologic impacts under climate change.

Crustal and upper mantle structures of Makran subduction zone, SE Iran by combined surface wave velocity analysis and gravity modeling

The inversion of Rayleigh wave group velocity dispersion curves is challenging, because it is non-linear and multimodal. In this study, we develop and test a new Rayleigh wave dispersion curve inversion scheme using the Shuffled Complex Evolution (SCE) algorithm. Incorporating this optimization algorithm into the inverse procedure not only can effectively locate the promising areas in the solution space for a global minimum but also avoids its wandering near the global minimum in the final stage of search. In addition, our approach differs from others in the model parameterization: Instead of subdividing the model into a large number of thin layers, we invert for thickness, velocities and densities and their vertical gradients of four layers, sediments, upper-crust, lower-crust and upper mantle. The proposed inverse procedure is applied to non-linear inversion of fundamental mode Rayleigh wave group dispersion curves for shear and compressional wave velocities. At first, to determine the efficiency and stability of the SCE method, two noise-free and two noisy synthetic data sets are inverted. Then real data for Makran region in SE Iran are inverted to examine the usage and robustness of the proposed approach on real surface wave data. In a second step, we applied 3D Gravity Modeling based on surface wave analysis results to obtain the density structure and thickness of each layer. The reason for using both types of data sets, is that gravity anomaly has a bad vertical resolution and surface wave group velocities are good for placing layer limits at depth, but they are not very sensitive to densities. Therefore, using gravity data increases the overall resolution of density distribution. In a final step, we used again the SCE method to invert the fundamental mode Rayleigh wave group dispersion curves based on the gravity results. Gravity results like thicknesses and sediment densities have been used to constrain the limit of search space in the SCE method. Results show a high shear and compressional velocity under the Gulf of Oman which reduce to the North of the Makran region. The Moho depth of the Oman Gulf is about 18–28 km and it increases to 46–48 km under the Taftan-Bazman volcanic-arc. The density image shows an average crustal density with maximum values under the Gulf of Oman decreasing northward to the Makran.

The effect of chemical reaction kinetic parameters on the bench-scale pyrolysis of lignocellulosic biomass

The pyrolysis of lignocellulosic biomass has received extensive attention due to its potential as an alternative and renewable energy source. The chemical reaction kinetic parameters, obtained by micro-scale thermogravimetric experiments and optimized by the Shuffled Complex Evolution method, are one of the key factors to represent the pyrolysis process. The bench-scale Fire Propagation Apparatus experiment with sample size of 0.1 m × 0.1 m is conducted to investigate the scale effect of these parameters during the pyrolysis process in a N2 environment. These optimized parameters are applied to the pyrolysis model based on Gypro considering the three-component parallel reaction mechanism, moisture and volume change to simulate the bench-scale experiment based on FireFOAM coupled with the dynamic mesh technology. Eventually, the predicted results agree well with experimental data, validating the effectiveness of the current parameters. Moreover, the effects of chemical reaction kinetic parameters from different references or models are further analyzed based upon the predicted results.

Case Study: On Objective Functions for the Peak Flow Calibration and for the Representative Parameter Estimation of the Basin

The objective function is usually used for verification of the optimization process between observed and simulated flows for the parameter estimation of rainfall–runoff model. However, it does not focus on peak flow and on representative parameter for various rain storm events of the basin, but it can estimate the optimal parameters by minimizing the overall error of observed and simulated flows. Therefore, the aim of this study is to suggest the objective functions that can fit peak flow in hydrograph and estimate the representative parameter of the basin for the events. The Streamflow Synthesis And Reservoir Regulation (SSARR) model was employed to perform flood runoff simulation for the Mihocheon stream basin in Geum River, Korea. Optimization was conducted using three calibration methods: genetic algorithm, pattern search, and the Shuffled Complex Evolution method developed at the University of Arizona (SCE-UA). Two objective functions of the Sum of Squared of Residual (SSR) and the Weighted Sum of Squared of Residual (WSSR) suggested in this study for peak flow optimization were applied. Since the parameters estimated using a single rain storm event do not represent the parameters for various rain storms in the basin, we used the representative objective function that can minimize the sum of objective functions of the events. Six rain storm events were used for the parameter estimation. Four events were used for the calibration and the other two for validation; then, the results by SSR and WSSR were compared. Flow runoff simulation was carried out based on the proposed objective functions, and the objective function of WSSR was found to be more useful than that of SSR in the simulation of peak flow runoff. Representative parameters that minimize the objective function for each of the four rain storm events were estimated. The calibrated observed and simulated flow runoff hydrographs obtained from applying the estimated representative parameters to two different rain storm events were better than those retrieved from parameters estimated using a single rain storm event. The results of this study demonstrated that WSSR is adequate in peak flow simulation, that is, the estimation of peak flood runoff. In addition, representative parameters can be applied to a flow runoff simulation for rain storm events that were not involved in parameter estimation.

Fast hydrological model calibration based on the heterogeneous parallel computing accelerated shuffled complex evolution method

ABSTRACTHydrological model calibration has been a hot issue for decades. The shuffled complex evolution method developed at the University of Arizona (SCE-UA) has been proved to be an effective and robust optimization approach. However, its computational efficiency deteriorates significantly when the amount of hydrometeorological data increases. In recent years, the rise of heterogeneous parallel computing has brought hope for the acceleration of hydrological model calibration. This study proposed a parallel SCE-UA method and applied it to the calibration of a watershed rainfall–runoff model, the Xinanjiang model. The parallel method was implemented on heterogeneous computing systems using OpenMP and CUDA. Performance testing and sensitivity analysis were carried out to verify its correctness and efficiency. Comparison results indicated that heterogeneous parallel computing-accelerated SCE-UA converged much more quickly than the original serial version and possessed satisfactory accuracy and stability for the task of fast hydrological model calibration.

Development and Application of Storage-Zone Decision Method for Long-Term Reservoir Operation Using the Dynamically Dimensioned Search Algorithm

A zone-based operation uses a simple method to make operational decisions based on rules established for storage zones. However, the division of a reservoir into appropriate storage zones involves complicated procedures. Using test functions to compare the three heuristic methods of a genetic algorithm, the shuffled complex evolution method developed by the University of Arizona, and the dynamically dimensioned search (DDS) method, we found that DDS might be useful for determining good global solutions to a problem with many decision variables. Hence, we applied the DDS method to determine three series of water levels for zoned reservoir storage division. The developed reservoir-operating method was applied to Andong Dam in the Republic of Korea. We derived zone boundaries using a generated dam inflow series and performed zone-based operations for validation using historical data under the assumption of known inflow data. The results showed improvements in the water supply reliability and vulnerability compared with historical data. The zone-based operating method derived from the present research could prove valuable because of its simplicity and practicality.

Quantifying dynamic sensitivity of optimization algorithm parameters to improve hydrological model calibration

Summary It is widely recognized that optimization algorithm parameters have significant impacts on algorithm performance, but quantifying the influence is very complex and difficult due to high computational demands and dynamic nature of search parameters. The overall aim of this paper is to develop a global sensitivity analysis based framework to dynamically quantify the individual and interactive influence of algorithm parameters on algorithm performance. A variance decomposition sensitivity analysis method, Analysis of Variance (ANOVA), is used for sensitivity quantification, because it is capable of handling small samples and more computationally efficient compared with other approaches. The Shuffled Complex Evolution method developed at the University of Arizona algorithm (SCE-UA) is selected as an optimization algorithm for investigation, and two criteria, i.e., convergence speed and success rate, are used to measure the performance of SCE-UA. Results show the proposed framework can effectively reveal the dynamic sensitivity of algorithm parameters in the search processes, including individual influences of parameters and their interactive impacts. Interactions between algorithm parameters have significant impacts on SCE-UA performance, which has not been reported in previous research. The proposed framework provides a means to understand the dynamics of algorithm parameter influence, and highlights the significance of considering interactive parameter influence to improve algorithm performance in the search processes.

New calibrated zonal model (POMA+) for temperature and airflow predictions

In building engineering and in the area of thermal environment, various modeling methods advanced to predict either the building energy consumption or airflow and temperature distribution within buildings. These methods are based on the different level of simplifications, the conservation equations used, the accuracy and the applications targeted. A new zonal model POMA+ has been developed to predict temperature and airflow distribution within any room of a building. The main objective of this work is to develop an evaluated and robust zonal model that can be used for building design and thermal analysis. This model has been evaluated by comparison to other models: existing zonal models and experimental data obtained from Minibat experimental chamber. The shuffled complex evolution method, as well as experimental results have been used together to calibrate the new zonal model and improve its prediction. The calibrated model shows a better prediction of airflow, temperature and pressure comparatively to the existing models for all case studies. Finally, multiple error measures have been used to evaluate the quality of the new calibrated model.

Optimum Parameters for Tuned Mass Damper Using Shuffled Complex Evolution (SCE) Algorithm

This study is investigated the optimum parameters for a tuned mass damper (TMD) under the seismic excitation. Shuffled complex evolution (SCE) is a meta-heuristic optimization method which is used to find the optimum damping and tuning frequency ratio for a TMD. The efficiency of the TMD is evaluated by decreasing the structural displacement dynamic magnification factor (DDMF) and acceleration dynamic magnification factor (ADMF) for a specific vibration mode of the structure. The optimum TMD parameters and the corresponding optimized DDMF and ADMF are achieved for two control levels (displacement control and acceleration control), different structural damping ratio and mass ratio of the TMD system. The optimum TMD parameters are checked for a 10-storey building under earthquake excitations. The maximum storey displacement and acceleration obtained by SCE method are compared with the results of other existing approaches. The results show that the peak building response decreased with decreases of about 20% for displacement and 30% for acceleration of the top floor. To show the efficiency of the adopted algorithm (SCE), a comparison is also made between SCE and other meta-heuristic optimization methods such as genetic algorithm (GA), particle swarm optimization (PSO) method and harmony search (HS) algorithm in terms of success rate and computational processing time. The results show that the proposed algorithm outperforms other meta-heuristic optimization methods.

Multi-model ensemble hydrologic prediction and uncertainties analysis

Abstract. Modelling uncertainties (i.e. input errors, parameter uncertainties and model structural errors) inevitably exist in hydrological prediction. A lot of recent attention has focused on these, of which input error modelling, parameter optimization and multi-model ensemble strategies are the three most popular methods to demonstrate the impacts of modelling uncertainties. In this paper the Xinanjiang model, the Hybrid rainfall–runoff model and the HYMOD model were applied to the Mishui Basin, south China, for daily streamflow ensemble simulation and uncertainty analysis. The three models were first calibrated by two parameter optimization algorithms, namely, the Shuffled Complex Evolution method (SCE-UA) and the Shuffled Complex Evolution Metropolis method (SCEM-UA); next, the input uncertainty was accounted for by introducing a normally-distributed error multiplier; then, the simulation sets calculated from the three models were combined by Bayesian model averaging (BMA). The results show that both these parameter optimization algorithms generate good streamflow simulations; specifically the SCEM-UA can imply parameter uncertainty and give the posterior distribution of the parameters. Considering the precipitation input uncertainty, the streamflow simulation precision does not improve very much. While the BMA combination not only improves the streamflow prediction precision, it also gives quantitative uncertainty bounds for the simulation sets. The SCEM-UA calculated prediction interval is better than the SCE-UA calculated one. These results suggest that considering the model parameters' uncertainties and doing multi-model ensemble simulations are very practical for streamflow prediction and flood forecasting, from which more precision prediction and more reliable uncertainty bounds can be generated.

Modeling water flows in a serial irrigation reservoir system considering irrigation return flows and reservoir operations

A water flows network modeling system was constructed to quantify water flows in the Balan Watershed, South Korea, which has two serial irrigation reservoirs. A modified version of the Synthetic Streamflow and Reservoir Regulation (SSARR) model was used to simulate the water flows, taking into account irrigation return flows and reservoir operations. The model parameters were calibrated using a heuristic search method, Shuffled Complex Evolution method developed at the University of Arizona (SCE-UA). The simulated streamflows and reservoir water levels were in good agreement with the observed. The irrigation return flows from paddy fields considerably affected the flow regimes of the streams. Specifically, the return flow rates of the irrigation water ranged from 28.0% to 35.0%. In addition, the water supply capacities of the irrigation reservoirs were evaluated using the modeling system, and joint operation rules were assessed. The results showed that these could have negative influences on the water supply of existing irrigation districts, and the potential effects of these rules on water management should be investigated. The modeling system is useful for identifying the states of water flows in multiple irrigation reservoir systems and for providing information about reservoir operations to water managers and stakeholders.

Combined Simulation-Optimization Model for Assessing Irrigation Water Supply Capacities of Reservoirs

This paper presents a combined simulation-optimization model for simulating reservoir operations without any detailed operation rules; it features the integration of a nonlinear, multiple-objective function and a heuristic search method, the Shuffled Complex Evolution method, developed at the University of Arizona. The model is applied to optimal water allocations from both Balan Reservoir and Seomjingang Dam in South Korea, an irrigation reservoir and a multipurpose, multioutlet reservoir, respectively, that primarily supply irrigation water. In the case of the optimal operation of Balan Reservoir, the simulation results show that the optimal release patterns are similar to those of historical operations because the demands for irrigation water are accurately predicted and guide optimal reservoir operations. In addition, the model is successfully applied to establishing a long-term reservoir operation plan. As for the optimal operation of Seomjingang Dam, the reservoir operations are affected by the target water stages, and the model provides reasonable results, irrespective of inflow conditions. Moreover, the model is employed to create a new operation rule that is necessary to adapt to changes in the circumstances related to water management. Consequently, it is concluded that the model is useful for assessing reservoirs’ irrigation water supply capacities when establishing operation plans and providing feasible alternatives for new operation rules, and it could be applied to real-time reservoir operations.

Parameter optimization of distributed hydrological model with a modified dynamically dimensioned search algorithm

A modified version of the dynamically dimensioned search (MDDS) is introduced for automatic calibration of watershed simulation models. The distinguishing feature of the MDDS is that the algorithm makes full use of sensitivity information in the optimization procedure. The Latin hypercube one-factor-at-a-time (LH-OAT) technique is used to calculate the sensitivity information of every parameter in the model. The performance of the MDDS is compared to that of the dynamically dimensioned search (DDS), the DDS identifying only the most sensitive parameters, and the shuffled complex evolution (SCE) method, respectively, for calibration of the easy distributed hydrological model (EasyDHM). The comparisons range from 500 to 5000 model evaluations per optimization trial. The results show the following: the MDDS algorithm outperforms the DDS algorithm, the DDS algorithm identifying the most sensitive parameters, and the SCE algorithm within a specified maximum number of function evaluations (fewer than 5000); the MDDS algorithm shows robustness compared with the DDS algorithm when the maximum number of model evaluations is less than 2500; the advantages of the MDDS algorithm are more obvious for a high-dimensional distributed hydrological model, such as the EasyDHM model; and the optimization results from the MDDS algorithm are not very sensitive to either the variance (between 0.3 and 1) for randn′ used in the MDDS algorithm or the number of strata used in the Latin hypercube (LH) sampling.

Effects of land use change on hydrological cycle from forest to upland field in a catchment, Japan

Understanding the effects of land use change on the hydrological cycle is very important for development of sustainable water resource in an upland field catchment. In this study, soil and hydrological properties in an upland field catchment, which was reclaimed partially from a forest catchment, were compared with another forest catchment. The soil properties of surface and subsurface layers were investigated in the two catchments. The soil was compacted and water-holding capacity of soil in the upland field catchment became smaller after the reclamation from forest to upland field, which decreased infiltration rate and water storage in the soil layers. We found that peak discharge and direct runoff in the upland field catchment increased compared with the forest catchment. Annual evapotranspiration from the upland field catchment tended to be lower due to the change in vegetation type and soil properties. Furthermore, a semi-distributed hydrological model was applied in the upland field catchment to understand the integrated effects of reclamation on the hydrological cycle. The model parameters, which were determined using a nonlinear optimization technique-the Shuffled Complex Evolution method (SCE), were compared between the two catchments. The Nash and Sutcliffe coefficient was used to evaluate the model performance. The simulated results indicated that evapotranspiration was decreased and change in discharge was more obvious in the surface layer. We considered that declined infiltration and water storage and increased peak discharge and direct runoff have a negative impact on water resources in the upland field catchment. This study will provide information for forest managers in planning and making decisions for land and water resource management.

Application of SCE-UA Approach to Economic Load Dispatch of Hydrothermal Generation System

The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydraulic network and water transport delay, which make the problem of finding global optimum difficult using standard optimization methods. This paper presents a new approach to the solution of optimal power generation to short-term hydrothermal scheduling problem, using shuffled complex evolution (SCE-UA) method. The proposed method introduces the new concept of competitive evolution and complex shuffling, which ensure that the information on the parameter space gained by each of individual complexes is shared throughout the entire population. This conducts an efficient search of the parameter space. In this study, the hydrothermal scheduling is formulated as an objective problem that maximizes the social welfare. Penalty function is proposed to handle the equality, inequality constraints especially active power balance constraint and ramp rate constraints. The simulation results reveal that SCE-UA effectively overcomes the premature phenomenon and improves the global convergence and optimization searching capability. It is a relatively consistent, effective and efficient optimization method in solving the short-term hydrothermal scheduling problem.

A methodology for estimating Leaf Area Index by assimilating remote sensing data into crop model based on temporal and spatial knowledge

In this paper, a methodology for Leaf Area Index (LAI) estimating was proposed by assimilating remote sensed data into crop model based on temporal and spatial knowledge. Firstly, sensitive parameters of crop model were calibrated by Shuffled Complex Evolution method developed at the University of Arizona (SCE-UA) optimization method based on phenological information, which is called temporal knowledge. The calibrated crop model will be used as the forecast operator. Then, the Taylor’s mean value theorem was applied to extracting spatial information from the Moderate Resolution Imaging Spectroradiometer (MODIS) multi-scale data, which was used to calibrate the LAI inversion results by A two-layer Canopy Reflectance Model (ACRM) model. The calibrated LAI result was used as the observation operator. Finally, an Ensemble Kalman Filter (EnKF) was used to assimilate MODIS data into crop model. The results showed that the method could significantly improve the estimation accuracy of LAI and the simulated curves of LAI more conform to the crop growth situation closely comparing with MODIS LAI products. The root mean square error (RMSE) of LAI calculated by assimilation is 0.9185 which is reduced by 58.7% compared with that by simulation (0.3795), and before and after assimilation the mean error is reduced by 92.6% which is from 0.3563 to 0.0265. All these experiments indicated that the methodology proposed in this paper is reasonable and accurate for estimating crop LAI.

Optimal Scheduling of Hydrothermal System with Network and Ramping via SCE-UA Method

This paper describes a method for scheduling large-scale hydrothermal power systems based on the shuffled complex evolution (SCE-UA) method. A multi-reservoir cascaded hydro-electric system with a non-linear relationship between water discharge rate, net head and power generation is considered. The water transport delay between connected reservoirs is also taken into account. SCE-UA is a successfully proven method in global optimization for many situations. Benefiting from its unique global optimization strategies into the inverse procedure greatly enhances the performance of SCE-UA method since it can not only effectively locate the promising areas in the solution space for a global minimum but also avoid its wandering near the global minimum in the final stage of search. The efficiency of the SCE-UA method is analyzed in terms of the mean performance and computational time, in comparison with the particle swarm optimization (PSO) algorithm. The simulation results reveal that SCE-UA effectively overcomes the premature phenomenon and improves the global convergence and optimization searching capability. It is a relatively consistent, effective and efficient optimization method in solving the large scale hydrothermal scheduling problem.

Bus holding strategy based on shuffled complex evolution method

Holding strategies are among the most commonly used operation control strategies. This paper presents an improved holding strategy. In the strategy, a mathematical model aiming to minimize the total waiting times of passengers at the current stop and at the following stops is constructed and a new heuristic algorithm, shuffled complex evolution method developed at the University of Arizona (SCEUA), is adopted to optimize the holding times of early buses. Results show that the improved holding strategy can provide better performance compared with a traditional schedule-based holding strategy and no-control strategy. The computational results are also evidence of the feasibility of using SCE-UA in optimizing the holding times of early buses at a stop.