Maximum Absolute Percentage Error Research Articles

English

Stochastic models have proven to be practically fundamental in fields such as science, economics, and business, among others. In Malawi, stochastic models have been used in fisheries to forecast fish catches. Nevertheless, forecasting water levels in major lakes and rivers in Malawi has been given little attention despite the availability of ample historical data. Although previous multichannel seismic surveys revealed the presence of low stands (sediment bypass zone) in Lake Malawi indicating that since the beginning of its formation, important water level fluctuations have been occurring, these previous surveys failed to predict and highlight much more clearly the status of these levels in the future. Therefore, the main objective of the study was to fill these research gaps. The study used Autoregressive (AR), Moving Average (MA), Autoregressive Moving Average (ARMA) and Autoregressive Integrated Moving Average (ARIMA) processes to select the appropriate stochastic model. Based on lowest Normalized Bayesian Information Criterion (NBIC), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Forecast Error (MFE), Maximum Absolute Percentage Error (MAXAPE), Maximum Absolute Error (MAXAE), and Mean Absolute Error (MAE) - ARIMA (0,1,1) model is found suitable for forecasting Lake Malawi water levels which shows negative trend up to 2035. The study further predicted that Lake Malawi water levels will decrease from the current average level of 472.97 m to an average of 468.63 m for the next 18 years (up to 2035). Key words: Forecasting, Lake Malawi, modelling, stochastic, time series, water levels.

Artificial intelligence based model for optimization of COD removal efficiency of an up-flow anaerobic sludge blanket reactor in the saline wastewater treatment.

The complex non-linear behavior presented in the biological treatment of wastewater requires an accurate model to predict the system performance. This study evaluates the effectiveness of an artificial intelligence (AI) model, based on the combination of artificial neural networks (ANNs) and genetic algorithms (GAs), to find the optimum performance of an up-flow anaerobic sludge blanket reactor (UASB) for saline wastewater treatment. Chemical oxygen demand (COD) removal was predicted using conductivity, organic loading rate (OLR) and temperature as input variables. The ANN model was built from experimental data and performance was assessed through the maximum mean absolute percentage error (= 9.226%) computed from the measured and model predicted values of the COD. Accordingly, the ANN model was used as a fitness function in a GA to find the best operational condition. In the worst case scenario (low energy requirements, high OLR usage and high salinity) this model guaranteed COD removal efficiency values above 70%. This result is consistent and was validated experimentally, confirming that this ANN-GA model can be used as a tool to achieve the best performance of a UASB reactor with the minimum requirement of energy for saline wastewater treatment.

G<sup>2</sup>EDPS's First Module & Its First Extension Modules

100% renewable worldwide power grid (Global Grid) system needs a Global Grid Electricity Demand Prediction System (G²EDPS) with very short, short, medium and long term forecasting consoles. This paper presents the 1^st core module and its 10 extension modules in the long term prediction console. A type 1 Mamdani like Fuzzy Inference System (FIS) with 7 triangle membership functions and 49 rules is designed for 2 input and 1 output variables for a 100 year forecasting period. The maximum absolute percentage errors (MAP), the mean absolute percentage errors (MAPE), and the Symmetric MAPE (SMAPE) of the best core module and its extension modules are respectively 0, 24; 0, 08; 0, 05 and 0, 22; 0, 07; 0, 05.

Accurate model to predict the solubility of fullerene C60 in organic solvents by using support vector regression

ABSTRACTThe support vector regression (SVR) combined with particle swarm optimization (PSO) for parameter optimization was successfully utilized to predict the solubility of fullerene C60 in various organic solvents via quantum/topological molecular descriptors. The prediction results strongly support that the generalization ability of SVR model consistently surpasses that of genetic algorithm-based multiple regression analysis (GA-MLRA) by applying identical training and test samples. Using leave-one-out cross validation (LOOCV) test via 122 samples, the maximum absolute percentage error (APE) does not exceed 3.87%, the mean absolute percentage error (MAPE) is only 0.62% and the correlation coefficient () is as high as 0.998. The results show that the estimated errors by SVR-LOOCV are quite smaller than those achieved by either GA-MLRA or SVR models. This study reveals the relationship between molecular descriptors of solvents and solubility of C60, and the constructed SVR model has already met the practical requirement in the prediction of the solubility of fullerene C60 in different solvents.

MODELAGEM E PROGNOSE DO PREÇO DE CARVÃO USANDO UM SISTEMA NEURO-FUZZY

RESUMO Utilizando dados da série temporal mensal de preços de carvão vegetal em Minas Gerais no período de janeiro de 2000 à setembro de 2014, este estudo teve como objetivo avaliar o uso do sistema neuro-fuzzy para modelagem e previsão de preços. Foram utilizados quatro estruturas de modelagem considerando diferentes defasagens da variável preço (1, 2, 3, 4 e 5 defasagens). A estrutura mais adequada para o sistema neuro-fuzzy foi escolhido com base nos valores de raiz quadrada do erro médio quadrático, erro médio absoluto, erro médio quadrático, erro médio percentual absoluto e máximo erro percentual absoluto para o período de previsão. Com os resultados encontrados, é possível concluir que um sistema neuro-fuzzy pode ser usado para prever corretamente os preços do carvão vegetal.

Modeling and predicting the tensile strength of poly (lactic acid)/graphene nanocomposites by using support vector regression

According to an experimental dataset under different process parameters, support vector regression (SVR) combined with particle swarm optimization (PSO) for its parameter optimization was employed to establish a mathematical model for prediction of the tensile strength of poly (lactic acid) (PLA)/graphene nanocomposites. Four variables, while graphene loading, temperature, time and speed, were employed as input variables, while tensile strength acted as output variable. Using leave-one-out cross validation test of 30 samples, the maximum absolute percentage error does not exceed 1.5%, the mean absolute percentage error (MAPE) is only 0.295% and the correlation coefficient [Formula: see text] is as high as 0.99. Compared with the results of response surface methodology (RSM) model, it is shown that the estimated errors by SVR are smaller than those achieved by RSM. It revealed that the generalization ability of SVR is superior to that of RSM model. Meanwhile, multifactor analysis is adopted for investigation on significances of each experimental factor and their influences on the tensile strength of PLA/graphene nanocomposites. This study suggests that the SVR model can provide important theoretical and practical guide to design the experiment, and control the intensity of the tensile strength of PLA/graphene nanocomposites via rational process parameters.

Semi-empirical calculation for design of flexural mode silicon mechanical resonator with variable cross section

This paper newly proposes a semi-empirical calculation for design of electrostatically driven flexural mode silicon (Si) mechanical resonators with a variable cross section which is applicable to a feasibility study of their development without finite element analysis (FEA). In the design for Si mechanical resonators with a variable cross section, a mode function describing a shape of vibration is simply assumed to be a static deflection function, and a resonant frequency is derived by applying the Rayleigh-Ritz method. The static deflection function, which reflects an effect of stress concentration generated by a variation of cross section, is semi-empirically formulated using some FEA results. This research adopts a clamped–clamped beam Si mechanical resonator which a wide rectangular bar located at the center is supported by same two narrow rectangular bars clamped to anchors. The resonant frequencies of the Si mechanical resonators are calculated within a mean absolute percentage error of 3% from the FEA results. In order to confirm the applicability of the semi-empirical formula, twenty different sizes of clamped–clamped beam Si mechanical resonators having the first-mode resonant frequency of 5–20MHz are designed and fabricated from a silicon-on-insulator (SOI) wafer, and their vibration characteristics in a vacuum environment are measured by a network analyzer. From the comparison with the measured resonant frequency of each Si mechanical resonator, the mean and maximum absolute percentage errors of the semi-empirical calculation are 28.6 and 51.3%, respectively, which are not negligible errors for the feasibility study. The fabricated Si mechanical resonators are different from an ideal clamped–clamped beam due to undercuts of the insulator layer under the anchors. The resonant frequency of each Si mechanical resonator is analyzed by the FEA model taking into account the effect of the undercuts. The mean and maximum absolute percentage errors of the FEA results from the measured ones are reduced to 9.61 and 19.9%, respectively. These results show that the large errors of the semi-empirical calculation are mainly caused by the undercuts, i.e., flexural stiffness degradation at both clamped ends. Under the condition that the FEA results obtained from FEA models precisely imitating actual geometry and boundary condition are used in the semi-empirical calculation, this is adequately applicable to the feasibility study for developing the Si mechanical resonator with a variable cross section.

Statistical variability comparison in MODIS and AERONET derived aerosol optical depth over Indo-Gangetic Plains using time series modeling

A lot of studies in the literature of Aerosol Optical Depth (AOD) done by using Moderate Resolution Imaging Spectroradiometer (MODIS) derived data, but the accuracy of satellite data in comparison to ground data derived from ARrosol Robotic NETwork (AERONET) has been always questionable. So to overcome from this situation, comparative study of a comprehensive ground based and satellite data for the period of 2001–2012 is modeled. The time series model is used for the accurate prediction of AOD and statistical variability is compared to assess the performance of the model in both cases. Root mean square error (RMSE), mean absolute percentage error (MAPE), stationary R-squared, R-squared, maximum absolute percentage error (MAPE), normalized Bayesian information criterion (NBIC) and Ljung–Box methods are used to check the applicability and validity of the developed ARIMA models revealing significant precision in the model performance. It was found that, it is possible to predict the AOD by statistical modeling using time series obtained from past data of MODIS and AERONET as input data. Moreover, the result shows that MODIS data can be formed from AERONET data by adding 0.251627±0.133589 and vice-versa by subtracting. From the forecast available for AODs for the next four years (2013–2017) by using the developed ARIMA model, it is concluded that the forecasted ground AOD has increased trend.

Modeling and optimization of a pharmaceutical crystallization process by using neural networks and genetic algorithms

Crystallization processes are extremely important in pharmaceutical science since they affect both the solid-state properties of the drug substances, and the drug product stability and performance. The crystallization stage must guarantee the quality of the product by assuring high purity, desired particle size distribution and crystalline morphology. This paper presents the use of artificial neural networks (ANNs) in combination with genetic algorithms (GAs) to model the complex process and identify the main parameters to optimize the crystallization of a specific pharmaceutical product in order to achieve substantial improvement in the quality of the product. Temperature, water content, volume, concentration and time addition of solvents, pH, and stirring speed were defined as inputs to build the ANN model to predict the crystal density. The ANN was able to learn the nonlinear relationships between structural information of the crystal and the main parameters of the process from an experimental set; the maximum mean absolute percentage error for the predicted values was 7.22%. The GA provided an optimal solution to define the operational conditions to take from a crystal density value of 0.61 to 0.737gcm−3 which represents a significant improvement in the physical and crystallographic properties. Experimental evaluations were carried out directly in the production plant obtaining crystal density values near the predicted one.

A Methodology for Wind Energy Evaluation in Complex Terrain Regions of Sarawak

Wind power is the safest, cleanest resource and has emerged as the speediest growing renewable energy in terms of annual installed capacity. Before a wind-drive system is set up, thorough wind resource assessment (WRA) must be conducted. In this paper, a methodology based on ground-station and topographical neural network modeled data is proposed to study the wind energy potential, in the monitored location and areas not covered by directly measurement instrumentation at Kuching. A new topographical feed forward neural network (T-FFNN) back propagation trained with Levenberg-Marquardt (LM), which consists of three layers was used to model the wind speed profile. The daily 10 m height, average hourly measured wind speed data for a period of ten years (2003-2012) for eight stations operated by Malaysia Meteorological Department (MMD) were used for the training, testing and validation. The geographical, meteorological and synthesized topographical parameters were used as input data, whereas the monthly wind speeds as the objective function. The optimum topology with maximum mean absolute percentage error of 6.4 % and correlation value of 0.9946 between the reference measured and predicted was obtained. The predicted monthly wind speed varied from 1.3-1.98 m/s with an average annual wind speed of 1.62 m/s. The characteristics of ground -based station was analyzed and presented. It was found in all the areas examined that the wind power falls within a low power density class (PD ≤ 100w/m2 ). Results from the micro-sizing showed an annual energy output (AEO) in the range of 4-12 MWh/year.

Modeling of active beam units with Modelica

This paper proposes an active beam model suitable for building energy simulations with the programming language Modelica. The model encapsulates empirical equations derived by a novel active beam terminal unit that operates with low-temperature heating and high-temperature cooling systems. Measurements from a full-scale experiment are used to compare the thermal behavior of the active beam with the one predicted by simulations. The simulation results show that the model corresponds closely with the actual operation. The model predicts the outlet water temperature of the active beam with a maximum mean absolute error of 0.18 °C. In term of maximum mean absolute percentage error, simulation results differ by 0.9%. The methodology presented is general enough to be applied for modeling other active beam units.

Monthly Energy Consumption Forecasting Based On Windowed Momentum Neural Network

Artificial Neural Network (ANN) with adaptability and non-linearity is well suited to perform forecasting tasks. The paper proposes the systematic approach of monthly energy forecasting using Windowed Momentum Algorithm in ANN. It describes the mathematical foundations and implementation to calculate the monthly energy demand using previous three years consecutive monthly energy data and weather information. The results are compared with the standard momentum, generally used in Back Propagation Algorithm. The proposed algorithm shows good accuracy with maximum mean absolute percentage error of 1.177%.

Solar energy potential assessment of western Himalayan Indian state of Himachal Pradesh using J48 algorithm of WEKA in ANN based prediction model

Solar potential of western Himalayan Indian state of Himachal Pradesh is assessed using Artificial Neural Network (ANN) based global solar radiation (GSR) prediction model. J48 algorithm in Waikato Environment for Knowledge Analysis (WEKA)is used for the selection of input parameters for ANN model for predicting GSR. Most relevant input parameters are found to be temperature, altitude and sunshine hours whereas latitude, longitude, clearness index and extraterrestrial radiation are found to be least influencing variables. The usefulness of J48 algorithm in variable selection is checked by developing five ANN models: ANN-1, ANN-2, ANN-3, ANN-4 and ANN-5. The maximum mean absolute percentage error (MAPE) for ANN-1, ANN-2, ANN-3, ANN-4 and ANN-5 are found to be 16.91%, 16.89%, 16.38%, 6.89% and 9.04% respectively. ANN-5 model is used to develop the solar maps of Himachal Pradesh. The estimated GSR varies from 3.59 to 5.38 kWh/m2/day indicating good solar potential for solar energy applications. A correlation is developed between NASA satellite data and ground measured GSR data to find values close to ground measured GSR for different locations. The correlation coefficient is found to be 0.97. Models developed can be used to assess solar potential of any location worldwide.

Water quality management using statistical analysis and time-series prediction model

This paper deals with water quality management using statistical analysis and time-series prediction model. The monthly variation of water quality standards has been used to compare statistical mean, median, mode, standard deviation, kurtosis, skewness, coefficient of variation at Yamuna River. Model validated using R-squared, root mean square error, mean absolute percentage error, maximum absolute percentage error, mean absolute error, maximum absolute error, normalized Bayesian information criterion, Ljung–Box analysis, predicted value and confidence limits. Using auto regressive integrated moving average model, future water quality parameters values have been estimated. It is observed that predictive model is useful at 95 % confidence limits and curve is platykurtic for potential of hydrogen (pH), free ammonia, total Kjeldahl nitrogen, dissolved oxygen, water temperature (WT); leptokurtic for chemical oxygen demand, biochemical oxygen demand. Also, it is observed that predicted series is close to the original series which provides a perfect fit. All parameters except pH and WT cross the prescribed limits of the World Health Organization /United States Environmental Protection Agency, and thus water is not fit for drinking, agriculture and industrial use.

Estimation of Solar Radiation by Artificial Networks: East Coast Malaysia

In this paper the solar radiation forecasting in Pekan located in Pahang is presented. The time series utilized are 10 minute solar radiation data obtained directly from the measurements realized in the sites during about one month. In order to do solar radiation forecasting, quick propagation algorithms Artificial Neural Network (ANN) models were developed. Around 1617 data's are taken to train ANN. The effects of temperature, humidity, wind speed, wind chill, pressure and rain on solar radiation are discussed in this paper. The maximum mean absolute percentage error was found to be less than 7.74% and R-squared (R2) values were found to be about 98.9% for the testing stations. However, these values were found to be 5.398% and 97.9% for the training stations. The trained and tested ANN models show greater accuracy for evaluating the solar radiation. The predicted solar potential values from the ANN are given in the form of table where included the other variables such as temperature, humidity, wind speed, wind chill, pressure and rain. This table is of prime importance for different working disciplines, like scientists, architects, meteorologists and solar engineers, in Malaysia. The predictions from the ANN models could enable scientists to locate and design solar energy systems in Malaysia and determine the best solar technology

SUPPORT VECTOR REGRESSION MODEL FOR DIRECT METHANOL FUEL CELL

The purpose of this paper is to establish a direct methanol fuel cell (DMFC) prediction model by using the support vector regression (SVR) approach combined with particle swarm optimization (PSO) algorithm for its parameter selection. Two variables, cell temperature and cell current density were employed as input variables, cell voltage value of DMFC acted as output variable. Using leave-one-out cross-validation (LOOCV) test on 21 samples, the maximum absolute percentage error (APE) yields 5.66%, the mean absolute percentage error (MAPE) is only 0.93% and the correlation coefficient (R2) as high as 0.995. Compared with the result of artificial neural network (ANN) approach, it is shown that the modeling ability of SVR surpasses that of ANN. These suggest that SVR prediction model can be a good predictor to estimate the cell voltage for DMFC system.

ELECTRICAL POWER PREDICTION OF PROTON EXCHANGE MEMBRANE FUEL CELL BY USING SUPPORT VECTOR REGRESSION

Studies have shown that numerous operating parameters affecting the proton exchange membrane fuel cell (PEMFC) performance, such as fuel cell operating temperature, operating pressure, anode/cathode humidification temperatures, anode/cathode stoichiometric flow ratios. In order to improve performance of fuel cell systems, it is advantageous to have an accurate model with which one can predict fuel cell behavior at different operating conditions. In this paper, a model using support vector regression (SVR) approach combining with particle swarm optimization (PSO) algorithm for its parameter optimization was developed to modeling and predicting the electrical power of proton exchange membrane fuel cell. The accuracy and reliability of the constructed support vector regression model are validated by leave-one-out cross-validation. Prediction results show that the maximum absolute percentage error does not exceed 5%, the mean absolute percentage error (MAPE) reached 0.68% and the correlation coefficient (R2) as high as 0.998. This implies that one can estimate an available combination of controller parameters by using support vector regression model to get suitable electrical power of proton exchange membrane fuel cell system.

Modeling and Predicting the Central Magnetic Flux Density of the Superconducting Solenoid Surrounded with Iron Yoke via SVR

A novel machine learning method based on support vector regression (SVR) approach, combined with a particle swarm optimization (PSO) algorithm for its parameter optimization, was proposed to predict the magnetic field in the centre of a superconducting solenoid surrounded by a cold iron yoke in terms of the geometrical parameters of the yoke. The leave-one-out cross validation (LOOCV) test results of SVR reveal that the prediction ability of the SVR model is greater than that of the conventional multivariate nonlinear regression. The maximum absolute percentage error of 26 samples obtained by SVR did not exceed 0.50% and the statistical mean absolute percentage error was solely 0.05%, which was quite accurate and satisfactory with the requirement of ultraprecision engineering and manufacturing. This investigation provides a clue that the hybrid PSO-SVR approach elaborated in this paper is a promising and practical methodology to precisely design the physical dimension of the iron yoke surrounded around the superconducting solenoid.

The application of fractal box dimensions in predicting the emission characteristics of colliding sawdust particles for sustainable sawmilling

The prediction of emission characteristics of sawdust particles immediately after the cutting operation from the interaction of band saw?s blade and plank is a growing research area. Still, a wide gap exists with respect to understanding the behaviour of sawdust particles as they collide with one another. Previous efforts have focused on non-collision states of sawdust particles. However, in real life, collision of particles must occur, with several particles colliding after the cutting operation. This paper establishes a new perspective of the fractal properties of sawdust particles in motion as a motivation to understanding how to control its toxicity of effects on sawmill workers and maintain sustainable sawmilling activities. In particular, the possibility of predicting the fractal dimension of the randomly moving sawdust particles in sawmills that is generated as fractal curves using the combination of probabilities and theoretical fractal dimensions is investigated for the first time. Cases were established on the possible representations of the theory and practice. As an example, four cases were designed around varied number of fractal pattern combinations drawn out of five and fifty different probabilities combinations, ten different random number generating seed values and maximum of four fractal curves generation iterations as driven parameters. Preliminary study of the differences between theoretical fractal box dimension recorded a maximum absolute percentage error of 7.24% for fractal curve associated with fractal pattern five (i.e. Koch 5). In all the cases studied, average absolute percentage error decreases between 3.52 � 1.18 and 1.51 � 1.14 while the correlation coefficient (R2) decreases between 0.9315 and 0.7365 from case 1 to case 4, respectively. It is concluded that the model is a good predictor of sawdust particle emission at colliding states from cutting operation. This is reflected in the fact that the higher the number of fractal patterns (generators) in a study case, the smaller the correlation coefficient between average estimated fractal box dimension and predicted fractal dimension of the sawdust particles in motion in the sawmill.

Mathematical representation of bolted-joint stiffness: A new suggested model

Joint member stiffness in a bolted connection directly influences the safety of a design in regard to both static and fatigue loading, as well as in the prevention of separation in the connection. This work provides a new simple model for computing the member stiffness in bolted connections for both fully and partially developed stress envelope fields. The new model is built using a stress distribution polynomial of third order. Finite element analysis (FEA) is performed for some joints geometries, and the results are used to estimate the best analytical envelope angle in the proposed analytical model that gives suitable convergence between the compared results. An experimental effort is exerted to validate the accuracy of a suggested model. When analytical results are compared with FEA results and experimental data, the maximum absolute percentage errors are found to be 2.69 and 14.69, respectively. Also, a good agreement is obtained when the analytical results are compared with other researchers’ results.