Minimum Mean Absolute Percentage Error Research Articles

An ERAFNN Prediction of Concrete Compressive Strength Based on Physical Properties of Electric Arc Furnace Oxidizing Slag

In this study, exact radial basis function neural network (ERBFNN) was used to predict the concrete compressive strength based on physical properties of electric arc furnace oxidizing slag. The mean absolute percentage error (MAPE) was used to evaluate the predicting performance. The results indicated the minimum MAPE of 0.08 % and 5.28 % could be achieved when training and predicting, respectively. According to the results, it revealed that ERBFNN was an efficiently tool for providing information.

Electricity Load Forecasting using Hybrid of Multiplicative Double Seasonal Exponential Smoothing Model with Artificial Neural Network

Electricity load forecasting often has many properties such as the nonlinearity, double seasonal cycles, and others those may be obstacles for the accuracy of forecasting using some classical statistical models. Many papers in this field have proposed using double seasonal (DS) exponential smoothing model to forecast. These papers indicated that electricity load forecasting using DS exponential smoothing model has better fit. Using artificial neural network (ANN) as a modern approach may be used for superior fitted forecasting, since this approach can deal with the non-linearity components of load data. The purpose of this paper is to improve the electricity load forecasting by building the hybrid model that includes a double seasonal exponential smoothing with an artificial neural network. This hybrid model will study the double seasonal effects and non-linearity components together based on the electricity load data. The strategy of building this hybrid model is by entering ANN output as an input in double seasonal exponential smoothing model. The data sets are taken from three stations with different electricity load characteristics such as a residential, industrial and city center. The electricity load testing forecast of DS exponential smoothing-ANN hybrid model gave the most minimum mean absolute percentage error (MAPE) measurement comparing with the electricity load testing forecasts of DS exponential smoothing and ANN for all electricity load data sets. In conclusion, DS exponential smoothing-ANN hybrid model are the most fitted for every electricity load data which contains the double seasonal effects and non-linearity components.

Predicting Hardness of Four Groundwater Monitoring Stations in Kaohsiung City of Taiwan Using Seven Types of GM (1, 1) Model

In this study, seven types of first-order and one-variable grey differential equation model (abbreviated as GM (1, 1) model) were used to predict the hardness of four groundwater monitoring stations in Kaohsiung City of Taiwan. The mean absolute percentage error (MAPE) was used to evaluate the predicting performance. The results indicated the minimum MAPE of 4.71 %, 3.15 %, 2.66 %, and 16.63 % could be achieved when predicting hardness of Fonsi, Datung, Shaukang, and Chihsien stations, respectively. According to the results, it revealed that GM (1, 1) was an efficiently early warning tool for providing groundwater quality information to the competent authority.

A 24‐h Forecast of Oxidant Concentration in Tokyo Using Neural Network and Fuzzy Learning Approach

AbstractIn this study, several types of adaptive network‐based fuzzy inference system (ANFIS) with different membership functions (MFs) and artificial neural network (ANN) were employed to predict hourly photochemical oxidants that were oxidizing substances such as ozone and peroxiacetyl nitrate produced by photochemical reactions. The results indicated that ANFIS statistically outperforms ANN in terms of hourly oxidant prediction. The minimum mean absolute percentage errors (MAPEs) of 4.99% could be achieved using ANFIS with bell shaped MFs. The maximum correlation coefficient, the minimum mean square errors, and the minimum root mean square errors were 0.99, 0.15, and 0.39, respectively. ANFIS's architecture consists of both ANN and fuzzy logic including linguistic expression of MFs and if‐then rules, so it can overcome the limitations of traditional neural network and increase the prediction performance.

Forecasting Hourly Roadside Particulate Matter in Taipei County of Taiwan Based on First‐Order and One‐Variable Grey Model

AbstractIn this study, seven types of first‐order and one‐variable grey differential equation model (abbreviated as GM (1, 1) model) were used to forecast hourly roadside particulate matter (PM) including PM10 and PM2.5 concentrations in Taipei County of Taiwan. Their forecasting performance was also compared. The results indicated that the minimum mean absolute percentage error (MAPE), mean squared error (MSE), root mean squared error (RMSE), and maximum correlation coefficient (R) was 11.70%, 60.06, 7.75, and 0.90%, respectively when forecasting PM10. When forecasting PM2.5, the minimum MAPE, MSE, RMSE, and maximum R‐value of 16.33%, 29.78, 5.46, and 0.90, respectively could be achieved. All statistical values revealed that the forecasting performance of GM (1, 1, x(0)), GM (1, 1, a), and GM (1, 1, b) outperformed other GM (1, 1) models. According to the results, it revealed that GM (1, 1) was an efficiently early warning tool for providing PM information to the roadside inhabitants.

A Global Optimization Algorithm for Minimizing Mean Absolute Percentage Error of Nonlinear Forecasting Model

In order to establish a high-precision nonlinear forecasting model, the paper presents a new global optimization technique for parameters optimization in nonlinear forecasting model based on the minimization of mean absolute percentage error (MAPE). By implementation of an optimization technique based on the successive use of a genetic algorithm and of a sequential quadratic programming (SQP) method: the genetic algorithm is used to perform a preliminary search in the solution space for locating the neighborhood of the solution, then, parameters optimization of nonlinear forecasting model is formulated as the minimax optimization problem by a transition, the SQP method is employed to solve minimax optimization problem for refining the best solution provided by the genetic algorithm, thus achieving the final optimal model and minimum MAPE. Three realworld examples are used to examine the simulation accuracy of the proposed method, the results show that the proposed method can improve the simulation precision compared to the existing algorithm.

Predicting effluent from the wastewater treatment plant of industrial park based on fuzzy network and influent quality

In this study, three types of adaptive neuro fuzzy inference system (ANFIS) were employed to predict effluent suspended solids (SS eff), chemical oxygen demand (COD eff), and pH eff from a wastewater treatment plant in industrial park. For comparison, artificial neural network (ANN) was also used. The results indicated that ANFIS statistically outperformed ANN in terms of effluent prediction. The minimum mean absolute percentage errors of 2.67%, 2.80%, and 0.42% for SS eff, COD eff, and pH eff could be achieved using ANFIS. The maximum values of correlation coefficient for SS eff, COD eff, and pH eff were 0.96, 0.93, and 0.95, respectively. The minimum mean square errors of 0.19, 2.25, and 0.00, and the minimum root mean square errors of 0.43, 1.48, and 0.04 for SS eff, COD eff, and pH eff could also be achieved. ANFIS’s architecture can overcome the limitations of traditional neural network. It also revealed that the influent indices could be applied to the prediction of effluent quality.

Mid-Term Load Forecasting Based on Neural Network Algorithm: a Comparison of Models

This article purposes the model of mid-term energy consumption load forecasting (MTLF) by using artificial neural network based on the two and the three years ahead. This load demand forecasting is a useful tool for a unit commitment and a fuel reserve planning in the power system. Both two and three years ahead forecasting uses two patterns for comparing the accuracy in this research. The results show the two years ahead of load forecasting, model no.2 can be reduced error which Mean Absolute Percentage Error (MAPE) is 4.35%. In three years ahead, the load forecasting model no.1 and no.2, MAPE are almost equal which are equal 4.65% and 4.70%, respectively. Finally, the experimental results show two and three years ahead for the load forecasting by using differential models and a varies number of a neuron in the hidden layer for finding the minimum MAPE of each model.

Prediction of effluent quality of a paper mill wastewater treatment using an adaptive network-based fuzzy inference system

Advanced neuro-fuzzy modeling, namely an adaptive network-based fuzzy inference system (ANFIS), was employed to develop models for the prediction of suspended solids (SS) and chemical oxygen demand (COD) removal of a full-scale wastewater treatment plant treating process wastewaters from a paper mill. In order to improve the network performance, fuzzy subtractive clustering was used to identify model's architecture and optimize fuzzy rule, meanwhile principal component analysis (PCA) was applied to reduce the input variable dimensionality. Input variables were reduced from six to four for COD and SS models, by considering PCA results and linear correlation matrices among input and output variables. The results indicate that reasonable forecasting and control performances have been achieved through the developed system. The minimum mean absolute percentage errors of 1.003% and 0.5161% for COD eff and SS eff could be achieved using ANFIS. The maximum correlation coefficient values for COD eff and SS eff were 0.9912 and 0.9882, respectively. The minimum mean square errors of 1.2883 and 0.0342, and the minimum RMSEs of 1.135 and 0.1849 for COD eff and SS eff could also be achieved.

Forecasting Construction Manpower Demand by Gray Model

Construction is a labor-intensive industry that is heavily reliant on the availability of local manpower. The construction workload also fluctuates in either a cyclical or random manner. As a result, there is always either a shortage or surplus of manpower. Although a number of good forecasting models have been developed, they require input of sufficient and good-quality data to produce accurate results. The aim of this paper is to explore the use of the gray model in forecasting construction manpower based on a limited amount of data. A wide range of forecasting models in the literature is first reviewed. A single-variable first-order gray model is then proposed to forecast construction manpower one quarter ahead. The model is tested using manpower data based on the Quarterly Report on General Household Survey published by the Census and Statistics Department of the HKSAR Government. Data from 64 quarters, covering the first quarter of 1992 to the fourth quarter of 2007, are included. A computer program is formulated to manipulate all of the calculations involved. Based on the minimum mean absolute percentage error (MAPE) criterion, it is found that the optimal sample size is 5. Based on the input of data from five quarters, the MAPE of the overall forecast is only 3.21%, and the maximum absolute percentage error is 8.92%. It is thus concluded that the gray model produces very accurate results. The results of this study also suggest that this model is applicable to forecasts of other time series particularly when limited data are available.

Using Seven Types of GM (1, 1) Model to Forecast Hourly Particulate Matter Concentration in Banciao City of Taiwan

In this study, seven types of first-order and one-variable grey differential equation model (abbreviated as GM (1, 1) model) were used to predict hourly particulate matter (PM) including PM10 and PM2.5 concentrations in Banciao City of Taiwan. Their prediction performance was also compared. The results indicated that the minimum mean absolute percentage error (MAPE), mean squared error (MSE), root mean squared error (RMSE), and maximum correlation coefficient (R) was 14.10%, 25.62, 5.06, and 0.96, respectively, when predicting PM10. When predicting PM2.5, the minimum MAPE, MSE, RMSE, and maximum R value of 15.24%, 11.57, 3.40, and 0.93, respectively, could be achieved. All statistical values revealed that the predicting performance of GM (1, 1, x(0)), GM (1, 1, a), and GM (1, 1, b) outperformed other GM (1, 1) models. According to the results, it revealed that GM (1, 1) GM (1, 1) was an efficiently early warning tool for providing PM information to the inhabitants.

The application of artificial neural networks to mapping of wind speed profile for energy application in Nigeria

Modelling and prediction of wind speed are essential prerequisites in the sitting and sizing of wind power applications. The profile of wind speed in Nigeria is modelled using artificial neural network (ANN). The ANN model consists of 3-layered, feed-forward, back-propagation network with different configurations, designed using the Neural Toolbox for MATLAB. The monthly mean daily wind speed data monitored at 10 m above ground level for a period of 20 years (1983–2003) for 28 ground stations operated by the Nigeria Meteorological Services (NIMET) were used as training (18 stations) and testing (10 stations) dataset. The geographical parameters (latitude, longitude and altitude) and the month of the year were used as input data, while the monthly mean wind speed was used as the output of the network. The optimum network architecture with minimum Mean Absolute Percentage Error (MAPE) of 8.9% and correlation coefficient ( r) between the predicted and the measured wind speed values of 0.9380 was obtained. The predicted monthly wind speed ranged from 0.9–13.1 m/s with an annual mean of 4.7 m/s. The model predicted wind speed values are given in the form of monthly maps, which can be easily used for assessment of wind energy potential for different locations within Nigeria.

Prediction of the effluent from a domestic wastewater treatment plant of CASP using gray model and neural network.

When a domestic wastewater treatment plant (DWWTP) is put into operation, variations of the wastewater quantity and quality must be predicted using mathematical models to assist in operating the wastewater treatment plant such that the treated effluent will be controlled and meet discharge standards. In this study, three types of gray model (GM) including GM (1, N), GM (1, 1), and rolling GM (1, 1) were used to predict the effluent biochemical oxygen demand (BOD), chemical oxygen demand (COD), and suspended solids (SS) from the DWWTP of conventional activated sludge process. The predicted results were compared with those obtained using backpropagation neural network (BPNN). The simulation results indicated that the minimum mean absolute percentage errors of 43.79%, 16.21%, and 30.11% for BOD, COD, and SS could be achieved. The fitness was higher when using BPNN for prediction of BOD (34.77%), but it required a large quantity of data for constructing model. Contrarily, GM only required a small amount of data (at least four data) and the prediction results were analogous to those of BPNN, even lower than that of BPNN when predicting COD (16.21%) and SS (30.11%). According to the prediction, results suggested that GM could predict the domestic effluent variation when its effluent data were insufficient.

Using fuzzy inference system to improve neural network for predicting hospital wastewater treatment plant effluent

In this study, three types of adaptive neuro fuzzy inference system (ANFIS) and artificial neural network (ANN) were employed to predict suspended solids (SS eff) and chemical oxygen demand (COD eff) in the effluent from a hospital wastewater treatment plant. The results indicated that ANFIS statistically outperforms ANN in terms of effluent prediction. The minimum mean absolute percentage errors of 11.99% and 12.75% for SS eff and COD eff could be achieved using ANFIS. The maximum values of correlation coefficient for SS eff and COD eff were 0.75 and 0.92, respectively. The minimum mean square errors of 0.17 and 19.58, and the minimum root mean square errors of 0.41 and 4.42 for SS eff and COD eff could also be achieved. ANFIS's architecture consists of both ANN and fuzzy logic including linguistic expression of membership functions and if–then rules, so it can overcome the limitations of traditional neural network and increase the prediction performance.

Improving neural network prediction of effluent from biological wastewater treatment plant of industrial park using fuzzy learning approach

Three types of adaptive network-based fuzzy inference system (ANFIS) in which the online monitoring parameters served as the input variable were employed to predict suspended solids (SS(eff)), chemical oxygen demand (COD(eff)), and pH(eff) in the effluent from a biological wastewater treatment plant in industrial park. Artificial neural network (ANN) was also used for comparison. The results indicated that ANFIS statistically outperforms ANN in terms of effluent prediction. When predicting, the minimum mean absolute percentage errors of 2.90, 2.54 and 0.36% for SS(eff), COD(eff) and pH(eff) could be achieved using ANFIS. The maximum values of correlation coefficient for SS(eff), COD(eff), and pH(eff) were 0.97, 0.95, and 0.98, respectively. The minimum mean square errors of 0.21, 1.41 and 0.00, and the minimum root mean square errors of 0.46, 1.19 and 0.04 for SS(eff), COD(eff), and pH(eff) could also be achieved.

Predicting performance of grey and neural network in industrial effluent using online monitoring parameters

Grey model (GM) and artificial neural network (ANN) were employed to predict suspended solids (SS eff), chemical oxygen demand (COD eff) and pH eff in the effluent from conventional activated process of an industrial wastewater treatment plant using simple online monitoring parameters (pH in the equalization pond effluent; pH, temperature, and dissolved oxygen in the aeration tank). The results indicated that the minimum mean absolute percentage errors of 20.79, 6.09 and 0.71% for SS eff, COD eff and pH eff, respectively, could be achieved using different types of GMs. GM only required a small amount of data (at least four data) and the prediction results were even better than those of ANN. According to the results, the online monitoring parameters could be applied on the prediction of effluent quality. It also revealed that GM could predict the industrial effluent variation as its effluent data was insufficient.

ARTIFICIAL INTELLIGENCE SOLUTION TO ELECTRICITY PRICE FORECASTING PROBLEM

The market-clearing prices in deregulated electricity markets are volatile. Good market-clearing price forecasting will help producers and consumers to prepare their corresponding bidding strategies so as to maximize their profits. Market-clearing price prediction is a difficult task since bidding strategies used by market participants are complicated and various uncertainties interact in an intricate way. This article proposes the use of two artificial neural networks: the first to predict the day-ahead load and the second to forecast the day-ahead market-clearing prices. The methodology is applied to the California power market. After determining the optimal artificial neural network architecture with the minimum mean absolute percentage error on the test set, this architecture is used for price forecasting in periods with price spikes, for price forecasting for weekends, and for week-ahead MCP forecasting during the four seasons of the year. The forecasting accuracy of the artificial neural network model is compared with the accuracy of the persistence method and the results prove the efficiency and practicality of the proposed technique.

Grey and neural network prediction of suspended solids and chemical oxygen demand in hospital wastewater treatment plant effluent

Grey model (GM) and artificial neural network (ANN) was employed to predict suspended solids (SS) and chemical oxygen demand (COD) in the effluent from sequence batch reactors of a hospital wastewater treatment plant (HWWTP). The results indicated that the minimum mean absolute percentage errors (MAPEs) of 23.14% and 51.73% for SS and COD could be achieved using genetic algorithm ANN (GAANN). The minimum prediction accuracy of 23.14% and 55.11% for SS and COD could be achieved. Contrarily, GM only required a small amount of data and the prediction accuracy was analogous to that of GAANN. In the first type of application, the MAPE values of SS for model prediction using GM (1, N) and GM (1, 2) lay between 23.14% and 26.67%. The MAPE values of COD using GM (1, N) were smaller than those of GM (1, 2). The results showed that the fitness was good for both GM (1, N) and GM (1, 2) to predict SS. However, only GM (1, N) was better for COD prediction as comparing to GM (1, 2). In the second type application, the MAPE values of SS and COD prediction using GM (1, 1) and rolling GM (1, 1) (RGM, i.e., 8 data before the point at which was considered to be predicted were used to construct model) lay between 24–28% and 37–52%, respectively. Furthermore, it was observed that influent pH has affected effluent SS and COD significantly. It suggested that if the influent pH could be adjusted appropriately, a better effluent SS and COD could be obtained.

A note on minimizing absolute percentage error in combined forecasts

In this note, two new approaches of combined forecasts are proposed. One approach minimizes mean absolute percentage error while the other approach minimizes the maximum absolute percentage error. A goal programming model is used to obtain the weights to combine different forecasts to minimize the mean absolute percentage error. This formulation can be solved readily by any linear programming computer code. The other approach, minimizing the maximum absolute percentage error, can also be formulated as a goal programming model. Scope and purposeMean absolute percentage error has been widely used as a performance measure in forecasting. One of the major reasons for its popularity is that it is easy to interpret and understand and it becomes a good alternative to mean squared error. Our proposed linear programming models can provide solutions of the minimum mean absolute percentage error and the minimum of the maximum absolute percentage error in combined forecasts. The models we proposed could be solved readily by any linear programming computer code.