Mean Absolute Percentage Relative Error Research Articles

An Approximate Explicit Green–Ampt Infiltration Model for Cumulative Infiltration

Core Ideas Proposed an explicit Green–Ampt model (EGA model) to estimate cumulative 1D vertical infiltration. The form of error term ε is determined as a power‐function through non‐dimensional numerical analysis. The EGA model is reliable for estimation the cumulative infiltration for a variety of soil textures. Accurately estimating soil moisture infiltration information contributes to scientific understanding of the one‐dimensional (1D) vertical infiltration process. Because of its simple form, the Green–Ampt (GA) model has been extensively employed to simulate soil infiltration processes. However, the GA model is an implicit solution that must be solved through iterative techniques, and thus is inconvenient. Therefore, based on the two‐parameter infiltration equation proposed by Valiantzas, by adding an error term and non‐dimensional numerical analysis, this study proposes an approximate explicit Green–Ampt model (EGA model) for estimating cumulative infiltration with a determined power function expression for the error term. A total of 12 typical soils were selected from the USDA soil textural classes, and the 1D vertical soil infiltration process was simulated using Hydrus‐1D. The reliability of the proposed EGA model was verified using measured and simulated values. The mean absolute percentage relative error (MAPRE) and percentage of bias (PB) were taken as evaluation indicators to compare the estimated cumulative infiltration with the measured and simulated values. The results revealed that all cumulative infiltration values estimated by the EGA model are in good agreement with those measured in laboratory experiments and simulated using Hydrus‐1D; the mean MAPRE and PB values of all treatments were 4.2 and 0.7%, respectively. In addition, the estimated errors of the EGA model were consistent with those of the GA model. Hence, the EGA model can estimate the cumulative infiltration in 1D vertical soil infiltration with high accuracy and is suitable for a variety of soil textures.

Comparative efficiency of different artificial intelligence based models for predicting density dependent saltwater intrusion processes in coastal aquifers and saltwater intrusion management utilizing the best performing model

Artificial intelligence based data driven models are useful tools in approximating density dependent coupled flow and salt transport processes in coastal aquifer systems. These emulators often serve as computationally efficient substitutes of rigorous numerical simulation models within a linked simulation-optimization (S/O) methodology. In this study, fuzzy c-means clustering based fuzzy inference systems (FIS) and adaptive network based fuzzy inference systems (ANFIS) are proposed to approximate the physical processes of an illustrative coastal aquifer system. FIS and ANFIS based models are also utilized to identify the most influential input variables in predicting salinity concentrations at three monitoring locations (C1, C2, and C3). Solution results obtained are compared with those obtained using a genetic programming (GP) based modelling approach. Performance evaluation results show that the developed FIS and ANFIS models perform equally well on training and testing datasets. It is also demonstrated that performances of both the FIS and ANFIS models are better than that of GP based models. Root mean square error (RMSE) and mean absolute percentage relative error (MAPRE) values obtained by using GP are larger than those obtained by both ANFIS and FIS models. The maximum prediction errors of GP represented by RMSE and MAPRE at the three monitoring locations are 22.43 mg/l and 2.84% respectively. On the other hand, GP results in lowest values of correlation coefficient (0.96) and Nash-Sutcliffe efficiency coefficient (0.91). FIS model outperforms both ANFIS and GP models in terms of a more detailed comparison criteria, including computation time and model complexity. FIS requires only 0.65 min for training in order to predict salinity concentrations at all three locations C1, C2, and C3. For the similar purpose, ANFIS and GP require 17.35 min and 276.5 min, respectively. Therefore, FIS model can be successfully applied as a computationally efficient substitute of complex numerical simulation models for predicting coupled flow and salt transport processes. Such applications can be very useful in developing a computationally feasible linked S/O methodology for regional scale management of saltwater intrusion in coastal aquifers. Results of the management model using the best performing global FIS model indicates that FIS model provides acceptable, accurate, and reliable groundwater extraction patterns to limit the saltwater concentrations within the pre-specified maximum allowable limits.

Modeling and simulation controlling system of HVAC using fuzzy and predictive (radial basis function, RBF) controllers

Heating, ventilating and air conditioning (HVAC) systems are used in buildings, industry and agriculture to provide thermal and humidity comfort. Modeling of HVAC system can help to design precise controlling systems. In this study, a HVAC system had been modeled using MATLAB simulation software that had been developed using a fuzzy controlling system and radial basis function (RBF) model of artificial neural network (ANN) as a predictive control system. Results of the modeled systems were extracted and compared with actual system. In order to compare results of the modeled and actual systems, comparing parameters, such as mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage/relative error (MAPE) and coefficient of Pearson correlation (r) were applied. The results indicated that, the modeled systems was accurately controlling the system and the difference between real and modeled system was also close. In the results as a whole, the predictive controller (RBF network) has the best performance compared to fuzzy model.

Modeling and optimization of parameters of flow rate of paddy rice grains through the horizontal rotating cylindrical drum of drum seeder

An experimental investigation was conducted to model the complex flow rate of paddy rice grains through the orifices on the circumference of the horizontal rotating cylindrical drum of a hand tractor drawn or self-propelled drum seeder using regression analysis and Artificial Neural Network (ANN). The dimensional analysis approach was followed to develop various dimensionless terms and study their effect on the flow rate. In the range of parameters studied, it was observed that the flow rate of paddy rice grains through the orifices of the drum increased with increase in Froude number and decreased with increase in orifice spacing to diameter ratio and drum fill ratio. A 4-9-5-1 neural network was found to predict the flow rate better than regression equation with overall mean absolute percentage relative error of 4.85%. Optimization technique based on Fast Non-dominated Sorting Genetic Algorithm (NSGA-II) was used to determine the levels of drum–grain-operating parameters for achieving the optimum flow rate to obtain the seed rate of 80 kg/ha with minimum deviation from its mean value with emptying of drum. The optimum drum configuration was found to be the one with 36 orifices of 6 mm diameter on its circumference. The drum was required to be initially filled to the extent of 53% of its total volume. Optimum speed of rotation of drum was 61 rpm which resulted in the forward speed of operation of 4.60–6.90 km/h if the forward speed of operation to peripheral speed of drum is in the range of 2:1 to 3:1. The outcome of the study will be useful for precise planting operation and the development of suitable systems for maintaining uniformity of seeding under field conditions.